sound travel solids

How Sound Travels Through Solids, Liquids and Gases

• August 13, 2022

We love to work with sound. Many of us record our own music, podcast, or other forms of sound. Knowing how sound travels through different mediums will allow you to have better control over the sound that you generate. That is what we will be looking at today. How does sound travel through solids, liquids, and gases? 

Can the way that you produce sound and the medium that it moves in make a difference in the volume that you will hear? How does this change when it comes to the different mediums? Will the furniture in a room have any impact on the acoustics of the room? How can you change it to create the perfect recording environment? 

These are just some of the things that we will discuss today. Knowing how sound travels through solids, liquids and gases are not only interesting, but it can have an impact on the way we record sounds and how we change things up. 

Why Is the Way That Sound Travels Through Mediums Important? 

One of the main reasons why it is important to understand how sound acts, is that when you understand something better, you can control it. As a youngster, I loved swimming. I still do. But one of my main attractions was that underneath the water it was the one place where everything went quiet. It always felt like the world stopped and it was just me and complete calm. 

I loved my family but there was always so much going on that it was just a great place to just be with my own imagination and thoughts. I could make up imaginary worlds and people, and have millions of stories running through my mind. All because there was a lack of sound under the water. 

But in reality, when you look at how sound behaves in a liquid, scientifically, this should not be the case. In fact, there should be more sound under the water than there is in the fresh air. Why? And why doesn’t it work that way? I wanted to find out. 

For many of us who record sound, it is important to be connected to it. If you understand what makes something sound fuller, what makes a noise loud, and how things act, you can have better control and your recording will end up being closer to what you intended in the first place. 

You might be recording a podcast, but for some reason, your voice keeps sounding muffled, understanding sound can help you identify what the cause could be and how you can fix it. 

What Is Sound? 

To understand why sound acts differently in different mediums we first have to understand what sound is. 

First, you need to know that sound can not exist in a void. This is different from light that does travel through nothingness. That is why we can see light shining from space where there is a void and no atmosphere. But those that have been to space say it is completely quiet. It must be an almost eerie feeling. 

Sound happens when something creates a vibration. This is done through musical instruments, our voices, speakers, and many other things. This then causes the medium around it, like the water or the air, to also vibrate and carry this sound with them. Without a medium, sound would not exist. That is because the molecules of the medium react and bump into those next to it and this allows the sound to travel on. 

At the same time, the medium that is used will determine just how loud the sound will be, it will also determine how far can travel and how the sound will generally react. This is because different solutions will have molecules that are more or less densely packed. 

Your surroundings will have a big impact. People who create a sound studio try to make the acoustics of the room as powerful as possible. This should help you do that. 

Let us now look at the three mediums that sound can travel through, solids, liquids, and gases, and how they change the reaction of the sound. 

First up we can look at gasses. You might wonder why gasses are mentioned when speaking of mediums that sound can move in. You may be visualizing a bunch of fog at a concert that makes the lights look incredible and makes the crowd go wild. 

And that is one possibility of gasses that can be used as a medium for sound to travel through. But most of the time, our air is the only gas that sound needs to continue its vibration. 

What Is the Air Made Of? 

We have already mentioned that sound can not exist in a void. But we can hear each other when we speak out in the open. We can hear music when it is being played under the starry sky and we can even hear kids shouting in a park a block away . 

That is because most of the air in our atmosphere is made up of gasses. Our atmosphere is not just a void, or we wouldn’t be able to live here anyway, but is made up of lots of gasses we can’t see. The atmosphere is made up of 78% Nitrogen, and 21% Oxygen, and the rest is a mixture of carbon dioxide, neon, and hydrogen. 

This gives us all the ability to breathe without needing a space suit, but it also gives sound the ability to travel in our atmosphere. We make a vibration and the molecules of the gases that we can’t even see start to bump into each other and takes that vibration further, making it possible for us to hear sounds. It is pretty amazing when you think about it. 

How Does Sound Travel Through Gases? 

Gas is the medium that will have the slowest speed of sound of all of them. This is because the molecules of the gases surrounding us are expanded and far away from each other. The vibrations do get passed over to each other but it takes longer to do. 

This is also why we often need things that can amplify our sounds like a microphone when we are speaking to a bigger group of people. These help us to make the vibrations bigger and to allow them to travel further than we would have been able to achieve with only our voice. 

Some Things That Can Influence Sound in Gases 

Have you ever felt that things are so much quieter after a big snowstorm? How the world seems almost different then? Turns out it might not just be your imagination. This is because the volume and speed of sound can be impacted by the temperature of the air and in turn the gas that is surrounding us. 

At lower temperatures, the molecules move around quicker and they can vibrate quicker. The energy behind the sound can start to be lost and the sound will become quieter or be lost faster. 

At normal room temperatures, the speed of sound will be a lot higher than it would be in the exact same room when the temperature is at freezing. 

There are many different liquids that have a higher or lower density but for the most part, it is in water where we would be interested in hearing a sound. If we go swimming or put a small portable speaker close to the water, we would like to hear the sound as loud as possible. But it just doesn’t always work like that. 

Let’s see how sound reacts in water or other liquids. 

Sound In Water 

The molecules in water are a lot more tightly packed than it is in gas. That is why sound travels much faster in water than it would travel in the air. Sound can actually travel in water almost four times faster than it can be in the air. 

That is really impressive. And still, if you submerge your head underwater, you will hear the sound but it might sound muffled and not quite like the sound that you are used to. 

Why Humans Hear Muffled Sounds in Water 

The water molecules are more tightly packed and the energy that it uses to carry sound is transported faster. In theory, you should be able to hear noises a lot louder when you are underwater. But that is not how we perceive this sound. 

This is because our ears are created to listen to sounds in the air. We pick up on sounds through our ear canal and these sounds are then transported to the brain that makes sense of it all. When you only submerge your ears, sounds will sound very muffled since the ears can’t take these sounds along the ear canal. 

When you submerge your head fully suddenly the sound is clearer and louder. Although it could still be somewhat muffled compared to outside the water. Our heads contain a lot of water, and inside the water, it will be our tissue that picks up on the sound and detects it. 

You could try to plug your ears but it will have very little effect on the volume of the noise under the water. The sound is not traveling along those normal lines. 

At the same time, chances are that it is also very hard and almost impossible for you to figure out from which direction the sound is coming. When the sound travels along the normal route our brain has cues to determine if it comes from behind us or in front. But when the sound does not travel in those normal routes the brain has no way of telling us where it is coming from. 

For humans communicating through sound under the water is not so easy. That is why divers have always used hand signals to communicate with their diving partners and why some have even started to use microphones that connect them. Allowing for a much better communication route. 

We know that we can’t hear sound in the same way when we are inside water as when we are in the air. But what happens when we make a big sound inside the water, like shouting? Will someone that is on the outside be able to hear it clearly? 

This is unlikely. That is because the surface of the water almost acts as a mirror for sound. Instead of the vibration moving outside of the water it gets reflected back. Making sure that very little sound is heard outside. 

Animals In Water 

Our ears might be designed to hear in air, but fish and mammals that live in the ocean can take advantage of the speed of sound inside the water. They are adapted to hearing noise completely clearly inside the water. 

Since sound does travel quickly in water and they can hear it, they can use sounds to communicate over much larger distances than we are able to do with just our voice. Whales, for example, have been known to use their voice to communicate with other whales over massive distances in the ocean. The sound of a humpback whale can travel thousands of miles in the ocean.  It also helps that the vibrations they can create are much larger than the ones our own vocal cords can produce. 

Then finally there are solids and how sound reacts when they come into contact with a solid. Since sound starts to get muffled when there are a lot of solid objects in its path you would think that it travels a lot slower in solids. But surprisingly that is not the case. There are however reasons why it reacts in this way. 

The Speed of Sound in Solids 

A solid object is densely packed with its molecules. Each solid object will be a little bit different from the other depending on the material it is made of and how densely packed its molecules are. There are some materials that will work better as insolation to noise than others, but we will discuss the reason for this shortly. But for the most part, sound will travel a lot faster in solids than it will in both liquids and gasses.

This is because the source of the sound will create the vibration in the molecules of the sound and then these tightly packed molecules will quickly send the vibration further along. This means that the speed of sound is a lot faster when traveling in a solid object and that it will be a lot louder too. 

Often a solid object will be a good source of amplification for a sound that you would like to enhance. The sound through a brass bugle gets enhanced through the design of the object and also through the material it is made of.

Examples Of Sounds in Solids 

It can be hard to think of examples where solid objects are used to move sound and make it louder. Let’s discuss some simple examples of this. 

You can put an ear to a solid object like a table and then make a soft tapping sound on the table. Compare how you heard it when your ear is on the solid compared to how loud it is when you hear the sound through the air. You will be surprised by how clearly the sound is enhanced by listening to it through a solid object. 

Another great example of an experiment that many of us probably unknowingly did as children is a string telephone. You take two cups and a long line of string. The two cups are each connected to one side of the string, one person listens into one cup while another speaks into the cup at their end. 

In this experiment, the vibrations are created and enhanced by the shape of the cup. Then these vibrations are transferred with the help of a solid object, the string, and the other person can hear your message at the other end of the string. Without raising your voice or shouting. 

It is always amazing to see just how far this simple design can carry sound. Fun fact, the world record for the longest-ever string telephone, which was made with tin cans, was a whopping 796 feet long. That is almost the distance of three football fields. That is a long way for a piece of string and two cups to carry sound. 

Then another great example of a sound being a lot louder when it is carried through a solid object is sounds that you can hear in the air. For example, hearing the sound of a horse coming closer, its hooves beating down on the ground. 

It is already a pretty impressive sound when you hear it in normal circumstances. But try putting your head to the ground and listening to the approach in that way. The sound is much louder and you can almost feel the vibrations that are making the sound you hear. 

Why Does Sound Get Muffled Through a Door? 

We know now that sound travels much faster through solid objects than it does through gasses or liquids. You would think that a solid object like a wall or a door will enhance the sound but the opposite is true. A sound that is coming from a different room is more muffled. 

If there is a lot of noise outside your home, for example, the neighbors having a party, it works to close the doors and windows and the sound won’t bother you as much. Even if you only have standard windows and doors. 

How does that work? It works because the sound you are hearing does not originate from inside a solid object. It traveled through the air until it came to your door. There it encountered a solid object. And instead of making the vibrations louder this change in medium made the sound lose some of the energy that it was traveling with. This reduces the level of the noise and makes it less noticeable when there are doors that are closed. 

Why Rooms Echo 

This change in energy is also one of the reasons why a room will or won’t echo. When you go into an empty room there is a good chance that you can create an echo. That is because the empty room has no solid objects that break the energy of the noise down and stop it. 

The vibrations bump only against the walls and reflect back. If you have a room that is still echoing even after your furniture has been installed, then there might not be enough solid objects that stop the speed and the energy of the sound. Something like a carpet that can absorb the vibration can help to stop the echo in the room. 

How Sound Travels Through Solids, Liquids, and Gases 

Sound needs a medium that can take the vibrations and move them along, allowing us to hear the sounds that are being created. 

When it comes to the speed of sound, a solid object will allow the vibration to move much faster since it has the most densely packed molecules. It will also make the sound the loudest. After solids, liquids have the highest speed of sound. And then finally gas, that included our air since it is made up of gasses. 

When a sound is traveling through one medium like air and then encounters another, like a solid door, it loses some of its energy and some of the volume will be lost. That is why solid insulation against sound is still one of the best options despite solids being a good conductor of sound. 

We might not be able to take full advantage of the high speed of sound that can be found inside a liquid, but those living in the ocean sure can and that is why whale sounds can travel thousands of miles under the water. 

Knowing how sound reacts to different mediums will allow us to understand it better. And that means that you should have better control over your recordings and all the ways that you like to create your own very unique sounds.

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by Chris Woodford . Last updated: July 23, 2023.

Photo: Sound is energy we hear made by things that vibrate. Photo by William R. Goodwin courtesy of US Navy and Wikimedia Commons .

What is sound?

Photo: Sensing with sound: Light doesn't travel well through ocean water: over half the light falling on the sea surface is absorbed within the first meter of water; 100m down and only 1 percent of the surface light remains. That's largely why mighty creatures of the deep rely on sound for communication and navigation. Whales, famously, "talk" to one another across entire ocean basins, while dolphins use sound, like bats, for echolocation. Photo by Bill Thompson courtesy of US Fish and Wildlife Service .

Robert Boyle's classic experiment

Artwork: Robert Boyle's famous experiment with an alarm clock.

How sound travels

Artwork: Sound waves and ocean waves compared. Top: Sound waves are longitudinal waves: the air moves back and forth along the same line as the wave travels, making alternate patterns of compressions and rarefactions. Bottom: Ocean waves are transverse waves: the water moves back and forth at right angles to the line in which the wave travels.

The science of sound waves

Picture: Reflected sound is extremely useful for "seeing" underwater where light doesn't really travel—that's the basic idea behind sonar. Here's a side-scan sonar (reflected sound) image of a World War II boat wrecked on the seabed. Photo courtesy of U.S. National Oceanographic and Atmospheric Administration, US Navy, and Wikimedia Commons .

Whispering galleries and amphitheaters

Photos by Carol M. Highsmith: 1) The Capitol in Washington, DC has a whispering gallery inside its dome. Photo credit: The George F. Landegger Collection of District of Columbia Photographs in Carol M. Highsmith's America, Library of Congress , Prints and Photographs Division. 2) It's easy to hear people talking in the curved memorial amphitheater building at Arlington National Cemetery, Arlington, Virginia. Photo credit: Photographs in the Carol M. Highsmith Archive, Library of Congress , Prints and Photographs Division.

Measuring waves

Understanding amplitude and frequency, why instruments sound different, the speed of sound.

Photo: Breaking through the sound barrier creates a sonic boom. The mist you can see, which is called a condensation cloud, isn't necessarily caused by an aircraft flying supersonic: it can occur at lower speeds too. It happens because moist air condenses due to the shock waves created by the plane. You might expect the plane to compress the air as it slices through. But the shock waves it generates alternately expand and contract the air, producing both compressions and rarefactions. The rarefactions cause very low pressure and it's these that make moisture in the air condense, producing the cloud you see here. Photo by John Gay courtesy of US Navy and Wikimedia Commons .

Why does sound go faster in some things than in others?

Chart: Generally, sound travels faster in solids (right) than in liquids (middle) or gases (left)... but there are exceptions!

How to measure the speed of sound

Sound in practice, if you liked this article..., find out more, on this website.

• Electric guitars
• Speech synthesis
• Synthesizers

On other sites

• Explore Sound : A comprehensive educational site from the Acoustical Society of America, with activities for students of all ages.
• Sound Waves : A great collection of interactive science lessons from the University of Salford, which explains what sound waves are and the different ways in which they behave.

Educational books for younger readers

• Sound (Science in a Flash) by Georgia Amson-Bradshaw. Franklin Watts/Hachette, 2020. Simple facts, experiments, and quizzes fill this book; the visually exciting design will appeal to reluctant readers. Also for ages 7–9.
• Sound by Angela Royston. Raintree, 2017. A basic introduction to sound and musical sounds, including simple activities. Ages 7–9.
• Experimenting with Sound Science Projects by Robert Gardner. Enslow Publishers, 2013. A comprehensive 120-page introduction, running through the science of sound in some detail, with plenty of hands-on projects and activities (including welcome coverage of how to run controlled experiments using the scientific method). Ages 9–12.
• Cool Science: Experiments with Sound and Hearing by Chris Woodford. Gareth Stevens Inc, 2010. One of my own books, this is a short introduction to sound through practical activities, for ages 9–12.
• Adventures in Sound with Max Axiom, Super Scientist by Emily Sohn. Capstone, 2007. The original, graphic novel (comic book) format should appeal to reluctant readers. Ages 8–10.

Popular science

• The Sound Book: The Science of the Sonic Wonders of the World by Trevor Cox. W. W. Norton, 2014. An entertaining tour through everyday sound science.

Academic books

• Master Handbook of Acoustics by F. Alton Everest and Ken Pohlmann. McGraw-Hill Education, 2015. A comprehensive reference for undergraduates and sound-design professionals.
• The Science of Sound by Thomas D. Rossing, Paul A. Wheeler, and F. Richard Moore. Pearson, 2013. One of the most popular general undergraduate texts.

Text copyright © Chris Woodford 2009, 2021. All rights reserved. Full copyright notice and terms of use .

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Speed of Sound in Solids

Claudia Tiller, Spring 2023

This page discusses the speed of sound in various solids, how to calculate them, and examples of such calculations.

• 1 The Main Idea
• 2.1 A Mathematical Model
• 2.2 Speeds of Various Compositions
• 3.1 Theoretical
• 3.2 Numerical Example
• 4 Connectedness
• 6.1 Further reading
• 6.2 External links
• 7 References

The Main Idea

The speed of sound can be defines as the distance travelled per a unit of time by a sound wave as it travels through an elastic medium. Elasticity refers to the ability of a body to resist distorting influence and return to its original shape when that influence is removed.

Factors that control the speed that sound travels in solids is measured by the solid's density and elasticity, as they affect the vibrational energy of the sound. Overall, the way the solid is composed determines the sound's speed limit through that solid.

The Structure of Solids and Effects on Sound Travel

Mediums are composed of particles that can be closely knit together or spread apart. Solids are characterized by an arrangement of atoms, ions, or molecules, where these components are generally locked in their positions. The particles can also be defined as elastic or inelastic. Particles that are closer to each other allow sound to be transferred quicker through the medium. Since particles that are compressed closer together allow sound to travel faster, it can be reasoned that sound travels slower in air.

With an increase in density, the space between particles in the solid decreases. The smaller distance between particles, or interatomic distance, the higher the speed. With an increase in elasticity of the atoms that make up the object, the lower the speed of sound in the object. Particles that have a high elasticity take more time to return to their place once they received vibrational energy. However, if the solid is completely inelastic then the sound cannot travel through it.

The practicality of this concept is highly applicable. The human ear captures sound waves through the outer cartilage of the ear, called the Pinna. The sound waves then travel up the ear canal and arrive at the ear drum which vibrates from the sound waves. After traveling through the inner ear, the vibrations arrive at the Cochlea. The Cochlea transfers the vibrations into information that auditory nerves can analyze.

A Mathematical Model

The speed of sound in solids [math]\displaystyle{ {V_{s}} }[/math] can be determined by the equation. Young's Modulus is a measure of elasticity of an object, and it can be computed to solve for interatomic values, such as interatomic bond stiffness or interatomic bond length.

[math]\displaystyle{ {V_{s}} = d \cdot \sqrt{\frac{K_{s}}{m_{atom}}} }[/math]

Alternative speed equation:

[math]\displaystyle{ {V_{s}} = \sqrt{\frac{B}{\rho}} }[/math]

[math]\displaystyle{ ρ }[/math] = density

[math]\displaystyle{ B }[/math] = Bulks Modulus

Bulks Modulus = [math]\displaystyle{ {\frac {ΔP}{ΔV/V}} }[/math]

[math]\displaystyle{ d }[/math] = interatomic bond length

[math]\displaystyle{ K_{s} }[/math] = Interatomic bond stiffness

Youngs Modulus = ( [math]\displaystyle{ Y = K_{s}/d }[/math] )

Youngs Modulus: [math]\displaystyle{ Y ={\frac{Stress}{Strain}} }[/math]

[math]\displaystyle{ Stress = {\frac{F_{tension}}{Area_{Cross Sectional}}} }[/math]

[math]\displaystyle{ Strain = {\frac{ΔL_{wire}}{L_{0}}} }[/math]

Speeds of Various Compositions

Theoretical

Two metal rods are made of different elements. The interatomic spring stiffness of element A is four times larger than the interatomic spring stiffness for element B. The mass of an atom of element A is four times greater than the mass of an atom of element B. The atomic diameters are approximately the same for A and B. What is the ratio of the speed of sound in rod A to the speed of sound in rod B?

Solution: In this situation, the ratio of the speed of sound in rod A to the speed of sound in rod B is 1.

Looking at the formula for computing speed of sound in solids, [math]\displaystyle{ {V_{s}} = d \cdot \sqrt{\frac{K_{s}}{m_{atom}}} }[/math] , you see that velocity depends three factors, interatomic stiffness, the mass of one atom, and interatomic bond length. The two rods differences in atomic mass and interatomic stiffness offset each other when the equations are set equal, and the ratio is determined to be 1.

[math]\displaystyle{ d \cdot \sqrt{\frac{4 \cdot K_{s}}{m_{atom}}} = d \cdot \sqrt{\frac{4 \cdot K_{s}}{m_{atom}}} }[/math] After simplification [math]\displaystyle{ V_{s_{1}} = V_{s{2}} }[/math]

Numerical Example

The Young's Modulus value of silver is 7.75e+10, atomic mass of silver is 108 g/mole, and the density of silver is 10.5 g/cm3. Using this information, calculate the speed of sound in silver.

Solution: The key to solving this problem is to realize the micro-macro connection of Young's Modulus. You are given that Young's Modulus is equal to 7.75e+10, and we know that Youngs Modulus = ( [math]\displaystyle{ K_{s}/d }[/math] ). In this situation, we need to calculate the interatomic bond length and use it and our Young's Modulus value to determine our interatomic stiffness.

To solve for d , we use the given density of silver (10.5 g/cm3). Using the basic equation for volume in relation to density and mass ( [math]\displaystyle{ V=m*d }[/math] ), we can find d , since d is equal to the cube root of volume.

Once d is solved for, it can be plugged back into the the equation [math]\displaystyle{ Y = K_{s}/d }[/math] to solve for [math]\displaystyle{ K_{s} }[/math]

Now, we have solved for both interatomic bond length and stiffness. The only quantity in the final speed of sound equation we need is the mass of one atom, which can be determined using Avogardro's number and the atomic mass. [math]\displaystyle{ m_{atom} = }[/math] atomic mass / [math]\displaystyle{ 6.022e23 }[/math]

Now that all variables are solved for, we can substitute values into our [math]\displaystyle{ {V_{s}} = d \cdot \sqrt{\frac{K_{s}}{m_{atom}}} }[/math] equation.

[math]\displaystyle{ {V_{s}} = 1.6 \cdot 10^{-10} \cdot \sqrt{ \frac{78534.7}{1.79 \cdot 10^{-22}}} }[/math]

[math]\displaystyle{ {V_{s}} = 2723 }[/math] m/s

Connectedness

Computing the speed of sound in solids depends on a mass' interatomic properties, such as interatomic bond length. In this specific case, an object's elasticity depends on the interatomic bond length. There are many applications that connect to the ability to compute the speed of sounds.

Seismic and ultrasonic imaging are also fields that benefit greatly from the calculation of sound speeds in solids. Seismic imaging refers to capturing images of the subsurface structure of the Earth. Seismic waves can be generated by earthquakes or other sources. Engineers and scientists can then locate gas and oil reservoirs, monitor activity such as volcano eruptions, and geological formations. In ultrasonic imaging, ultrasonic waves can be sent through the body and have the time it takes to bounce back be measured. This then creates images of internal organs or tissues, used in cases such as prenatal imaging as well as medical diagnosing. In more specific fields such as in Industrial Engineering, these calculations could be applied to questions regarding how to build a soundproof area. It would therefore be optimal to select a solid with a low speed of sound velocity, with a solid that has tightly packed particles. There are many vast applications to this, as an object's ability to block or allow sound waves through it. However, some cases require contractors to build structures that allow sound to travel through. Material testing uses the calculation of sound in solids to determine mechanical properties of such materials. Engineers can then calculate the material's elasticity, stiffness, and other properties. Knowledge regarding how solids are structured and how they correlate with the speed of sounds in those solids are vital to building structures that meet the criteria.

Overall, being able to calculate the speed of sounds in solids has a wide range of applications in engineering, medicine, and science.

The speed of sound in air was first measured by Sir Isaac Newton, and first correctly computed by Pierre-Simon Laplace in 1816. Before this precise measurement, attempts had been made across Europe during the 1700s, most famously Reverend William Derham's experiment in 1709 across the town of Upminister, England. Reverend Derham used a shotgun's noise and several known landmarks around time to measure the time it took for the sound of the blast to be heard from select distances.

Young's Modulus was named after English physicist Thomas Young. In actuality, the concept was developed earlier by physicists Leonhard Euler and Giordano Riccati in the 1720s.

Youngs Modulus: [1] Interatomic Bonds: [2]

Further reading

Further Information can be found on the speed of sound in solids in Matter and Interactions, 4th Edition by Ruth W. Chabay & Bruce A. Sherwood

External links

Internet resources on this topic can be found at:

Engineering Tool Box [3]

Hyperphysics [4]

Potto Project [5]

NDT Resource Center [6]

The Engineering ToolBox [7]

Ear Image [8]

Yew Chung [9]

This section contains the the references used while writing this page

Chart from [10]

Matter and Interactions 4th Edition by Chabay and Sherwood

Wikipage created by Daiven Patel

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17.3: Speed of Sound

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Learning Objectives

• Explain the relationship between wavelength and frequency of sound
• Determine the speed of sound in different media
• Derive the equation for the speed of sound in air
• Determine the speed of sound in air for a given temperature

Sound, like all waves, travels at a certain speed and has the properties of frequency and wavelength. You can observe direct evidence of the speed of sound while watching a fireworks display (Figure \(\PageIndex{1}\)). You see the flash of an explosion well before you hear its sound and possibly feel the pressure wave, implying both that sound travels at a finite speed and that it is much slower than light.

The difference between the speed of light and the speed of sound can also be experienced during an electrical storm. The flash of lighting is often seen before the clap of thunder. You may have heard that if you count the number of seconds between the flash and the sound, you can estimate the distance to the source. Every five seconds converts to about one mile. The velocity of any wave is related to its frequency and wavelength by

\[v = f \lambda, \label{17.3}\]

where \(v\) is the speed of the wave, \(f\) is its frequency, and \(\lambda\) is its wavelength. Recall from Waves that the wavelength is the length of the wave as measured between sequential identical points. For example, for a surface water wave or sinusoidal wave on a string, the wavelength can be measured between any two convenient sequential points with the same height and slope, such as between two sequential crests or two sequential troughs. Similarly, the wavelength of a sound wave is the distance between sequential identical parts of a wave—for example, between sequential compressions (Figure \(\PageIndex{2}\)). The frequency is the same as that of the source and is the number of waves that pass a point per unit time.

Speed of Sound in Various Media

Table \(\PageIndex{1}\) shows that the speed of sound varies greatly in different media. The speed of sound in a medium depends on how quickly vibrational energy can be transferred through the medium. For this reason, the derivation of the speed of sound in a medium depends on the medium and on the state of the medium. In general, the equation for the speed of a mechanical wave in a medium depends on the square root of the restoring force, or the elastic property, divided by the inertial property,

\[v = \sqrt{\frac{\text{elastic property}}{\text{inertial property}}} \ldotp\]

Also, sound waves satisfy the wave equation derived in Waves ,

\[\frac{\partial^{2} y (x,t)}{\partial x^{2}} = \frac{1}{v^{2}} \frac{\partial^{2} y (x,t)}{\partial t^{2}} \ldotp\]

Recall from Waves that the speed of a wave on a string is equal to \(v = \sqrt{\frac{F_{T}}{\mu}}\), where the restoring force is the tension in the string F T and the linear density \(\mu\) is the inertial property. In a fluid, the speed of sound depends on the bulk modulus and the density,

\[v = \sqrt{\frac{B}{\rho}} \ldotp \label{17.4}\]

The speed of sound in a solid the depends on the Young’s modulus of the medium and the density,

\[v = \sqrt{\frac{Y}{\rho}} \ldotp \label{17.5}\]

In an ideal gas (see The Kinetic Theory of Gases ), the equation for the speed of sound is

\[v = \sqrt{\frac{\gamma RT_{K}}{M}}, \label{17.6}\]

where \(\gamma\) is the adiabatic index, R = 8.31 J/mol • K is the gas constant, T K is the absolute temperature in kelvins, and M is the molecular mass. In general, the more rigid (or less compressible) the medium, the faster the speed of sound. This observation is analogous to the fact that the frequency of simple harmonic motion is directly proportional to the stiffness of the oscillating object as measured by k, the spring constant. The greater the density of a medium, the slower the speed of sound. This observation is analogous to the fact that the frequency of a simple harmonic motion is inversely proportional to m, the mass of the oscillating object. The speed of sound in air is low, because air is easily compressible. Because liquids and solids are relatively rigid and very difficult to compress, the speed of sound in such media is generally greater than in gases.

Because the speed of sound depends on the density of the material, and the density depends on the temperature, there is a relationship between the temperature in a given medium and the speed of sound in the medium. For air at sea level, the speed of sound is given by

\[v = 331\; m/s \sqrt{1 + \frac{T_{C}}{273 °C}} = 331\; m/s \sqrt{\frac{T_{K}}{273\; K}} \label{17.7}\]

where the temperature in the first equation (denoted as T C ) is in degrees Celsius and the temperature in the second equation (denoted as T K ) is in kelvins. The speed of sound in gases is related to the average speed of particles in the gas,

\[v_{rms} = \sqrt{\frac{3k_{B}T}{m}}.\]

where \(k_B\) is the Boltzmann constant (1.38 x 10 −23 J/K) and m is the mass of each (identical) particle in the gas. Note that v refers to the speed of the coherent propagation of a disturbance (the wave), whereas \(v_{rms}\) describes the speeds of particles in random directions. Thus, it is reasonable that the speed of sound in air and other gases should depend on the square root of temperature. While not negligible, this is not a strong dependence. At 0°C , the speed of sound is 331 m/s, whereas at 20.0 °C, it is 343 m/s, less than a 4% increase. Figure \(\PageIndex{3}\) shows how a bat uses the speed of sound to sense distances.

Derivation of the Speed of Sound in Air

As stated earlier, the speed of sound in a medium depends on the medium and the state of the medium. The derivation of the equation for the speed of sound in air starts with the mass flow rate and continuity equation discussed in Fluid Mechanics . Consider fluid flow through a pipe with cross-sectional area \(A\) (Figure \(\PageIndex{4}\)). The mass in a small volume of length \(x\) of the pipe is equal to the density times the volume, or

\[m = \rho V = \rho Ax.\]

The mass flow rate is

\[\frac{dm}{dt} = \frac{d}{dt} (\rho V) = \frac{d}{dt} (\rho Ax) = \rho A \frac{dx}{dt} = \rho Av \ldotp\]

The continuity equation from Fluid Mechanics states that the mass flow rate into a volume has to equal the mass flow rate out of the volume,

\[\rho_{in} A_{in}v_{in} = \rho_{out} A_{out}v_{out}.\]

Now consider a sound wave moving through a parcel of air. A parcel of air is a small volume of air with imaginary boundaries (Figure \(\PageIndex{5}\)). The density, temperature, and velocity on one side of the volume of the fluid are given as \(\rho\), T, v, and on the other side are \(\rho\) + d\(\rho\), \(T + dT\), \(v + dv\).

The continuity equation states that the mass flow rate entering the volume is equal to the mass flow rate leaving the volume, so

\[\rho Av = (\rho + d \rho)A(v + dv) \ldotp\]

This equation can be simplified, noting that the area cancels and considering that the multiplication of two infinitesimals is approximately equal to zero: d\(\rho\)(dv) ≈ 0,

\[\begin{split} \rho v & = (\rho + d \rho)(v + dv) \\ & = \rho v + \rho (dv) + (d \rho)v + (d \rho)(dv) \\ 0 & = \rho (dv) + (d \rho) v \\ \rho\; dv & = -v\; d \rho \ldotp \end{split}\]

The net force on the volume of fluid (Figure \(\PageIndex{6}\)) equals the sum of the forces on the left face and the right face:

\[\begin{split} F_{net} & = p\; dy\; dz - (p + dp)\; dy\; dz \ & = p\; dy\; dz\; - p\; dy\; dz - dp\; dy\; dz \\ & = -dp\; dy\; dz \\ ma & = -dp\; dy\; dz \ldotp \end{split}\]

Figure \(\PageIndex{6}\):

The acceleration is the force divided by the mass and the mass is equal to the density times the volume, m = \(\rho\)V = \(\rho\) dx dy dz. We have

\[\begin{split} ma & = -dp\; dy\; dz \\ a & = - \frac{dp\; dy\; dz}{m} = - \frac{dp\; dy\; dz}{\rho\; dx\; dy\; dz} = - \frac{dp}{\rho\; dx} \\ \frac{dv}{dt} & = - \frac{dp}{\rho\; dx} \\ dv & = - \frac{dp}{\rho dx} dt = - \frac{dp}{\rho} \frac{1}{v} \\ \rho v\; dv & = -dp \ldotp \end{split}\]

From the continuity equation \(\rho\) dv = −vd\(\rho\), we obtain

\[\begin{split} \rho v\; dv & = -dp \\ (-v\; d \rho)v & = -dp \\ v & = \sqrt{\frac{dp}{d \rho}} \ldotp \end{split}\]

Consider a sound wave moving through air. During the process of compression and expansion of the gas, no heat is added or removed from the system. A process where heat is not added or removed from the system is known as an adiabatic system. Adiabatic processes are covered in detail in The First Law of Thermodynamics , but for now it is sufficient to say that for an adiabatic process, \(pV^{\gamma} = \text{constant}\), where \(p\) is the pressure, \(V\) is the volume, and gamma (\(\gamma\)) is a constant that depends on the gas. For air, \(\gamma\) = 1.40. The density equals the number of moles times the molar mass divided by the volume, so the volume is equal to V = \(\frac{nM}{\rho}\). The number of moles and the molar mass are constant and can be absorbed into the constant p \(\left(\dfrac{1}{\rho}\right)^{\gamma}\) = constant. Taking the natural logarithm of both sides yields ln p − \(\gamma\) ln \(\rho\) = constant. Differentiating with respect to the density, the equation becomes

\[\begin{split} \ln p - \gamma \ln \rho & = constant \\ \frac{d}{d \rho} (\ln p - \gamma \ln \rho) & = \frac{d}{d \rho} (constant) \\ \frac{1}{p} \frac{dp}{d \rho} - \frac{\gamma}{\rho} & = 0 \\ \frac{dp}{d \rho} & = \frac{\gamma p}{\rho} \ldotp \end{split}\]

If the air can be considered an ideal gas, we can use the ideal gas law:

\[\begin{split} pV & = nRT = \frac{m}{M} RT \\ p & = \frac{m}{V} \frac{RT}{M} = \rho \frac{RT}{M} \ldotp \end{split}\]

Here M is the molar mass of air:

\[\frac{dp}{d \rho} = \frac{\gamma p}{\rho} = \frac{\gamma \left(\rho \frac{RT}{M}\right)}{\rho} = \frac{\gamma RT}{M} \ldotp\]

Since the speed of sound is equal to v = \(\sqrt{\frac{dp}{d \rho}}\), the speed is equal to

\[v = \sqrt{\frac{\gamma RT}{M}} \ldotp\]

Note that the velocity is faster at higher temperatures and slower for heavier gases. For air, \(\gamma\) = 1.4, M = 0.02897 kg/mol, and R = 8.31 J/mol • K. If the temperature is T C = 20 °C (T = 293 K), the speed of sound is v = 343 m/s. The equation for the speed of sound in air v = \(\sqrt{\frac{\gamma RT}{M}}\) can be simplified to give the equation for the speed of sound in air as a function of absolute temperature:

\[\begin{split} v & = \sqrt{\frac{\gamma RT}{M}} \\ & = \sqrt{\frac{\gamma RT}{M} \left(\dfrac{273\; K}{273\; K}\right)} = \sqrt{\frac{(273\; K) \gamma R}{M}} \sqrt{\frac{T}{273\; K}} \\ & \approx 331\; m/s \sqrt{\frac{T}{273\; K}} \ldotp \end{split}\]

One of the more important properties of sound is that its speed is nearly independent of the frequency. This independence is certainly true in open air for sounds in the audible range. If this independence were not true, you would certainly notice it for music played by a marching band in a football stadium, for example. Suppose that high-frequency sounds traveled faster—then the farther you were from the band, the more the sound from the low-pitch instruments would lag that from the high-pitch ones. But the music from all instruments arrives in cadence independent of distance, so all frequencies must travel at nearly the same speed. Recall that

\[v = f \lambda \ldotp\]

In a given medium under fixed conditions, \(v\) is constant, so there is a relationship between \(f\) and \(\lambda\); the higher the frequency, the smaller the wavelength (Figure \(\PageIndex{7}\)).

Example \(\PageIndex{1}\): Calculating Wavelengths

Calculate the wavelengths of sounds at the extremes of the audible range, 20 and 20,000 Hz, in 30.0 °C air. (Assume that the frequency values are accurate to two significant figures.)

To find wavelength from frequency, we can use \(v = f \lambda\).

• Identify knowns. The value for \(v\) is given by \[v = 331\; m/s \sqrt{\frac{T}{273\; K}} \ldotp \nonumber\]
• Convert the temperature into kelvins and then enter the temperature into the equation \[v = 331\; m/s \sqrt{\frac{303\; K}{273\; K}} = 348.7\; m/s \ldotp \nonumber\]
• Solve the relationship between speed and wavelength for \(\lambda\): $$\lambda = \frac{v}{f} \ldotp \nonumber$$
• Enter the speed and the minimum frequency to give the maximum wavelength: \[\lambda_{max} = \frac{348.7\; m/s}{20\; Hz} = 17\; m \ldotp \nonumber\]
• Enter the speed and the maximum frequency to give the minimum wavelength: \[\lambda_{min} = \frac{348.7\; m/s}{20,000\; Hz} = 0.017\; m = 1.7\; cm \ldotp \nonumber\]

Significance

Because the product of \(f\) multiplied by \(\lambda\) equals a constant, the smaller \(f\) is, the larger \(\lambda\) must be, and vice versa.

The speed of sound can change when sound travels from one medium to another, but the frequency usually remains the same. This is similar to the frequency of a wave on a string being equal to the frequency of the force oscillating the string. If \(v\) changes and \(f\) remains the same, then the wavelength \(\lambda\) must change. That is, because \(v = f \lambda\), the higher the speed of a sound, the greater its wavelength for a given frequency.

Exercise \(\PageIndex{1}\)

Imagine you observe two firework shells explode. You hear the explosion of one as soon as you see it. However, you see the other shell for several milliseconds before you hear the explosion. Explain why this is so.

Although sound waves in a fluid are longitudinal, sound waves in a solid travel both as longitudinal waves and transverse waves. Seismic waves, which are essentially sound waves in Earth’s crust produced by earthquakes, are an interesting example of how the speed of sound depends on the rigidity of the medium. Earthquakes produce both longitudinal and transverse waves, and these travel at different speeds. The bulk modulus of granite is greater than its shear modulus. For that reason, the speed of longitudinal or pressure waves (P-waves) in earthquakes in granite is significantly higher than the speed of transverse or shear waves (S-waves). Both types of earthquake waves travel slower in less rigid material, such as sediments. P-waves have speeds of 4 to 7 km/s, and S-waves range in speed from 2 to 5 km/s, both being faster in more rigid material. The P-wave gets progressively farther ahead of the S-wave as they travel through Earth’s crust. The time between the P- and S-waves is routinely used to determine the distance to their source, the epicenter of the earthquake. Because S-waves do not pass through the liquid core, two shadow regions are produced (Figure \(\PageIndex{8}\)).

As sound waves move away from a speaker, or away from the epicenter of an earthquake, their power per unit area decreases. This is why the sound is very loud near a speaker and becomes less loud as you move away from the speaker. This also explains why there can be an extreme amount of damage at the epicenter of an earthquake but only tremors are felt in areas far from the epicenter. The power per unit area is known as the intensity, and in the next section, we will discuss how the intensity depends on the distance from the source.

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• The Human Ear

Since the speed of a wave is defined as the distance that a point on a wave (such as a compression or a rarefaction) travels per unit of time, it is often expressed in units of meters/second (abbreviated m/s). In equation form, this is

The faster a sound wave travels, the more distance it will cover in the same period of time. If a sound wave were observed to travel a distance of 700 meters in 2 seconds, then the speed of the wave would be 350 m/s. A slower wave would cover less distance - perhaps 660 meters - in the same time period of 2 seconds and thus have a speed of 330 m/s. Faster waves cover more distance in the same period of time.

Factors Affecting Wave Speed

The speed of any wave depends upon the properties of the medium through which the wave is traveling. Typically there are two essential types of properties that affect wave speed - inertial properties and elastic properties. Elastic properties are those properties related to the tendency of a material to maintain its shape and not deform whenever a force or stress is applied to it. A material such as steel will experience a very small deformation of shape (and dimension) when a stress is applied to it. Steel is a rigid material with a high elasticity. On the other hand, a material such as a rubber band is highly flexible; when a force is applied to stretch the rubber band, it deforms or changes its shape readily. A small stress on the rubber band causes a large deformation. Steel is considered to be a stiff or rigid material, whereas a rubber band is considered a flexible material. At the particle level, a stiff or rigid material is characterized by atoms and/or molecules with strong attractions for each other. When a force is applied in an attempt to stretch or deform the material, its strong particle interactions prevent this deformation and help the material maintain its shape. Rigid materials such as steel are considered to have a high elasticity. (Elastic modulus is the technical term). The phase of matter has a tremendous impact upon the elastic properties of the medium. In general, solids have the strongest interactions between particles, followed by liquids and then gases. For this reason, longitudinal sound waves travel faster in solids than they do in liquids than they do in gases. Even though the inertial factor may favor gases, the elastic factor has a greater influence on the speed ( v ) of a wave, thus yielding this general pattern:

Inertial properties are those properties related to the material's tendency to be sluggish to changes in its state of motion. The density of a medium is an example of an inertial property . The greater the inertia (i.e., mass density) of individual particles of the medium, the less responsive they will be to the interactions between neighboring particles and the slower that the wave will be. As stated above, sound waves travel faster in solids than they do in liquids than they do in gases. However, within a single phase of matter, the inertial property of density tends to be the property that has a greatest impact upon the speed of sound. A sound wave will travel faster in a less dense material than a more dense material. Thus, a sound wave will travel nearly three times faster in Helium than it will in air. This is mostly due to the lower mass of Helium particles as compared to air particles.  

The Speed of Sound in Air

The speed of a sound wave in air depends upon the properties of the air, mostly the temperature, and to a lesser degree, the humidity. Humidity is the result of water vapor being present in air. Like any liquid, water has a tendency to evaporate. As it does, particles of gaseous water become mixed in the air. This additional matter will affect the mass density of the air (an inertial property). The temperature will affect the strength of the particle interactions (an elastic property). At normal atmospheric pressure, the temperature dependence of the speed of a sound wave through dry air is approximated by the following equation:

where T is the temperature of the air in degrees Celsius. Using this equation to determine the speed of a sound wave in air at a temperature of 20 degrees Celsius yields the following solution.

v = 331 m/s + (0.6 m/s/C)•(20 C)

v = 331 m/s + 12 m/s

v = 343 m/s

(The above equation relating the speed of a sound wave in air to the temperature provides reasonably accurate speed values for temperatures between 0 and 100 Celsius. The equation itself does not have any theoretical basis; it is simply the result of inspecting temperature-speed data for this temperature range. Other equations do exist that are based upon theoretical reasoning and provide accurate data for all temperatures. Nonetheless, the equation above will be sufficient for our use as introductory Physics students.)

Look It Up!

Using wave speed to determine distances.

At normal atmospheric pressure and a temperature of 20 degrees Celsius, a sound wave will travel at approximately 343 m/s; this is approximately equal to 750 miles/hour. While this speed may seem fast by human standards (the fastest humans can sprint at approximately 11 m/s and highway speeds are approximately 30 m/s), the speed of a sound wave is slow in comparison to the speed of a light wave. Light travels through air at a speed of approximately 300 000 000 m/s; this is nearly 900 000 times the speed of sound. For this reason, humans can observe a detectable time delay between the thunder and the lightning during a storm. The arrival of the light wave from the location of the lightning strike occurs in so little time that it is essentially negligible. Yet the arrival of the sound wave from the location of the lightning strike occurs much later. The time delay between the arrival of the light wave (lightning) and the arrival of the sound wave (thunder) allows a person to approximate his/her distance from the storm location. For instance if the thunder is heard 3 seconds after the lightning is seen, then sound (whose speed is approximated as 345 m/s) has traveled a distance of

If this value is converted to miles (divide by 1600 m/1 mi), then the storm is a distance of 0.65 miles away.

Another phenomenon related to the perception of time delays between two events is an echo . A person can often perceive a time delay between the production of a sound and the arrival of a reflection of that sound off a distant barrier. If you have ever made a holler within a canyon, perhaps you have heard an echo of your holler off a distant canyon wall. The time delay between the holler and the echo corresponds to the time for the holler to travel the round-trip distance to the canyon wall and back. A measurement of this time would allow a person to estimate the one-way distance to the canyon wall. For instance if an echo is heard 1.40 seconds after making the holler , then the distance to the canyon wall can be found as follows:

The canyon wall is 242 meters away. You might have noticed that the time of 0.70 seconds is used in the equation. Since the time delay corresponds to the time for the holler to travel the round-trip distance to the canyon wall and back, the one-way distance to the canyon wall corresponds to one-half the time delay.

While an echo is of relatively minimal importance to humans, echolocation is an essential trick of the trade for bats. Being a nocturnal creature, bats must use sound waves to navigate and hunt. They produce short bursts of ultrasonic sound waves that reflect off objects in their surroundings and return. Their detection of the time delay between the sending and receiving of the pulses allows a bat to approximate the distance to surrounding objects. Some bats, known as Doppler bats, are capable of detecting the speed and direction of any moving objects by monitoring the changes in frequency of the reflected pulses. These bats are utilizing the physics of the Doppler effect discussed in an earlier unit (and also to be discussed later in Lesson 3 ). This method of echolocation enables a bat to navigate and to hunt.

The Wave Equation Revisited

Like any wave, a sound wave has a speed that is mathematically related to the frequency and the wavelength of the wave. As discussed in a previous unit , the mathematical relationship between speed, frequency and wavelength is given by the following equation.

Using the symbols v , λ , and f , the equation can be rewritten as

Check Your Understanding

1. An automatic focus camera is able to focus on objects by use of an ultrasonic sound wave. The camera sends out sound waves that reflect off distant objects and return to the camera. A sensor detects the time it takes for the waves to return and then determines the distance an object is from the camera. If a sound wave (speed = 340 m/s) returns to the camera 0.150 seconds after leaving the camera, how far away is the object?

Answer = 25.5 m

The speed of the sound wave is 340 m/s. The distance can be found using d = v • t resulting in an answer of 25.5 m. Use 0.075 seconds for the time since 0.150 seconds refers to the round-trip distance.

2. On a hot summer day, a pesky little mosquito produced its warning sound near your ear. The sound is produced by the beating of its wings at a rate of about 600 wing beats per second.

a. What is the frequency in Hertz of the sound wave? b. Assuming the sound wave moves with a velocity of 350 m/s, what is the wavelength of the wave?

Part a Answer: 600 Hz (given)

Part b Answer: 0.583 meters

3. Doubling the frequency of a wave source doubles the speed of the waves.

a. True b. False

Doubling the frequency will halve the wavelength; speed is unaffected by the alteration in the frequency. The speed of a wave depends upon the properties of the medium.

4. Playing middle C on the piano keyboard produces a sound with a frequency of 256 Hz. Assuming the speed of sound in air is 345 m/s, determine the wavelength of the sound corresponding to the note of middle C.

 Answer: 1.35 meters (rounded)

Let λ = wavelength. Use v = f • λ where v = 345 m/s and f = 256 Hz. Rearrange the equation to the form of λ = v / f. Substitute and solve.

5. Most people can detect frequencies as high as 20 000 Hz. Assuming the speed of sound in air is 345 m/s, determine the wavelength of the sound corresponding to this upper range of audible hearing.

Answer: 0.0173 meters (rounded)

Let λ = wavelength. Use v = f • λ where v = 345 m/s and f = 20 000 Hz. Rearrange the equation to the form of λ = v / f. Substitute and solve.

6. An elephant produces a 10 Hz sound wave. Assuming the speed of sound in air is 345 m/s, determine the wavelength of this infrasonic sound wave.

Answer: 34.5 meters

Let λ = wavelength. Use v = f • λ where v = 345 m/s and f = 10 Hz. Rearrange the equation to the form of λ = v / f. Substitute and solve.

7. Determine the speed of sound on a cold winter day (T=3 degrees C).

Answer: 332.8 m/s

The speed of sound in air is dependent upon the temperature of air. The dependence is expressed by the equation:

v = 331 m/s + (0.6 m/s/C) • T

where T is the temperature in Celsius. Substitute and solve.

v = 331 m/s + (0.6 m/s/C) • 3 C v = 331 m/s + 1.8 m/s v = 332.8 m/s

8. Miles Tugo is camping in Glacier National Park. In the midst of a glacier canyon, he makes a loud holler. He hears an echo 1.22 seconds later. The air temperature is 20 degrees C. How far away are the canyon walls?

Answer = 209 m

The speed of the sound wave at this temperature is 343 m/s (using the equation described in the Tutorial). The distance can be found using d = v • t resulting in an answer of 343 m. Use 0.61 second for the time since 1.22 seconds refers to the round-trip distance.

9. Two sound waves are traveling through a container of unknown gas. Wave A has a wavelength of 1.2 m. Wave B has a wavelength of 3.6 m. The velocity of wave B must be __________ the velocity of wave A.

a. one-ninth b. one-third c. the same as d. three times larger than

The speed of a wave does not depend upon its wavelength, but rather upon the properties of the medium. The medium has not changed, so neither has the speed.

10. Two sound waves are traveling through a container of unknown gas. Wave A has a wavelength of 1.2 m. Wave B has a wavelength of 3.6 m. The frequency of wave B must be __________ the frequency of wave A.

Since Wave B has three times the wavelength of Wave A, it must have one-third the frequency. Frequency and wavelength are inversely related.

• Interference and Beats

17.2 Speed of Sound

Learning objectives.

By the end of this section, you will be able to:

• Explain the relationship between wavelength and frequency of sound
• Determine the speed of sound in different media
• Derive the equation for the speed of sound in air
• Determine the speed of sound in air for a given temperature

Sound, like all waves, travels at a certain speed and has the properties of frequency and wavelength. You can observe direct evidence of the speed of sound while watching a fireworks display ( Figure 17.4 ). You see the flash of an explosion well before you hear its sound and possibly feel the pressure wave, implying both that sound travels at a finite speed and that it is much slower than light.

The difference between the speed of light and the speed of sound can also be experienced during an electrical storm. The flash of lighting is often seen before the clap of thunder. You may have heard that if you count the number of seconds between the flash and the sound, you can estimate the distance to the source. Every five seconds converts to about one mile. The velocity of any wave is related to its frequency and wavelength by

where v is the speed of the wave, f is its frequency, and λ λ is its wavelength. Recall from Waves that the wavelength is the length of the wave as measured between sequential identical points. For example, for a surface water wave or sinusoidal wave on a string, the wavelength can be measured between any two convenient sequential points with the same height and slope, such as between two sequential crests or two sequential troughs. Similarly, the wavelength of a sound wave is the distance between sequential identical parts of a wave—for example, between sequential compressions ( Figure 17.5 ). The frequency is the same as that of the source and is the number of waves that pass a point per unit time.

Speed of Sound in Various Media

Table 17.1 shows that the speed of sound varies greatly in different media. The speed of sound in a medium depends on how quickly vibrational energy can be transferred through the medium. For this reason, the derivation of the speed of sound in a medium depends on the medium and on the state of the medium. In general, the equation for the speed of a mechanical wave in a medium depends on the square root of the restoring force, or the elastic property , divided by the inertial property ,

Also, sound waves satisfy the wave equation derived in Waves ,

Recall from Waves that the speed of a wave on a string is equal to v = F T μ , v = F T μ , where the restoring force is the tension in the string F T F T and the linear density μ μ is the inertial property. In a fluid, the speed of sound depends on the bulk modulus and the density,

The speed of sound in a solid depends on the Young’s modulus of the medium and the density,

In an ideal gas (see The Kinetic Theory of Gases ), the equation for the speed of sound is

where γ γ is the adiabatic index, R = 8.31 J/mol · K R = 8.31 J/mol · K is the gas constant, T K T K is the absolute temperature in kelvins, and M is the molar mass. In general, the more rigid (or less compressible) the medium, the faster the speed of sound. This observation is analogous to the fact that the frequency of simple harmonic motion is directly proportional to the stiffness of the oscillating object as measured by k , the spring constant. The greater the density of a medium, the slower the speed of sound. This observation is analogous to the fact that the frequency of a simple harmonic motion is inversely proportional to m , the mass of the oscillating object. The speed of sound in air is low, because air is easily compressible. Because liquids and solids are relatively rigid and very difficult to compress, the speed of sound in such media is generally greater than in gases.

Because the speed of sound depends on the density of the material, and the density depends on the temperature, there is a relationship between the temperature in a given medium and the speed of sound in the medium. For air at sea level, the speed of sound is given by

where the temperature in the first equation (denoted as T C T C ) is in degrees Celsius and the temperature in the second equation (denoted as T K T K ) is in kelvins. The speed of sound in gases is related to the average speed of particles in the gas, v rms = 3 k B T m , v rms = 3 k B T m , where k B k B is the Boltzmann constant ( 1.38 × 10 −23 J/K ) ( 1.38 × 10 −23 J/K ) and m is the mass of each (identical) particle in the gas. Note that v refers to the speed of the coherent propagation of a disturbance (the wave), whereas v rms v rms describes the speeds of particles in random directions. Thus, it is reasonable that the speed of sound in air and other gases should depend on the square root of temperature. While not negligible, this is not a strong dependence. At 0 °C 0 °C , the speed of sound is 331 m/s, whereas at 20.0 °C 20.0 °C , it is 343 m/s, less than a 4 % 4 % increase. Figure 17.6 shows how a bat uses the speed of sound to sense distances.

Derivation of the Speed of Sound in Air

As stated earlier, the speed of sound in a medium depends on the medium and the state of the medium. The derivation of the equation for the speed of sound in air starts with the mass flow rate and continuity equation discussed in Fluid Mechanics .

Consider fluid flow through a pipe with cross-sectional area A ( Figure 17.7 ). The mass in a small volume of length x of the pipe is equal to the density times the volume, or m = ρ V = ρ A x . m = ρ V = ρ A x . The mass flow rate is

The continuity equation from Fluid Mechanics states that the mass flow rate into a volume has to equal the mass flow rate out of the volume, ρ in A in v in = ρ out A out v out . ρ in A in v in = ρ out A out v out .

Now consider a sound wave moving through a parcel of air. A parcel of air is a small volume of air with imaginary boundaries ( Figure 17.8 ). The density, temperature, and velocity on one side of the volume of the fluid are given as ρ , T , v , ρ , T , v , and on the other side are ρ + d ρ , T + d T , v + d v . ρ + d ρ , T + d T , v + d v .

The continuity equation states that the mass flow rate entering the volume is equal to the mass flow rate leaving the volume, so

This equation can be simplified, noting that the area cancels and considering that the multiplication of two infinitesimals is approximately equal to zero: d ρ ( d v ) ≈ 0 , d ρ ( d v ) ≈ 0 ,

The net force on the volume of fluid ( Figure 17.9 ) equals the sum of the forces on the left face and the right face:

The acceleration is the force divided by the mass and the mass is equal to the density times the volume, m = ρ V = ρ d x d y d z . m = ρ V = ρ d x d y d z . We have

From the continuity equation ρ d v = − v d ρ ρ d v = − v d ρ , we obtain

Consider a sound wave moving through air. During the process of compression and expansion of the gas, no heat is added or removed from the system. A process where heat is not added or removed from the system is known as an adiabatic system. Adiabatic processes are covered in detail in The First Law of Thermodynamics , but for now it is sufficient to say that for an adiabatic process, p V γ = constant, p V γ = constant, where p is the pressure, V is the volume, and gamma ( γ ) ( γ ) is a constant that depends on the gas. For air, γ = 1.40 γ = 1.40 . The density equals the number of moles times the molar mass divided by the volume, so the volume is equal to V = n M ρ . V = n M ρ . The number of moles and the molar mass are constant and can be absorbed into the constant p ( 1 ρ ) γ = constant . p ( 1 ρ ) γ = constant . Taking the natural logarithm of both sides yields ln p − γ ln ρ = constant . ln p − γ ln ρ = constant . Differentiating with respect to the density, the equation becomes

If the air can be considered an ideal gas, we can use the ideal gas law:

Here M is the molar mass of air:

Since the speed of sound is equal to v = d p d ρ v = d p d ρ , the speed is equal to

Note that the velocity is faster at higher temperatures and slower for heavier gases. For air, γ = 1.4 , γ = 1.4 , M = 0.02897 kg mol , M = 0.02897 kg mol , and R = 8.31 J mol · K . R = 8.31 J mol · K . If the temperature is T C = 20 ° C ( T = 293 K ) , T C = 20 ° C ( T = 293 K ) , the speed of sound is v = 343 m/s . v = 343 m/s .

The equation for the speed of sound in air v = γ R T M v = γ R T M can be simplified to give the equation for the speed of sound in air as a function of absolute temperature:

One of the more important properties of sound is that its speed is nearly independent of the frequency. This independence is certainly true in open air for sounds in the audible range. If this independence were not true, you would certainly notice it for music played by a marching band in a football stadium, for example. Suppose that high-frequency sounds traveled faster—then the farther you were from the band, the more the sound from the low-pitch instruments would lag that from the high-pitch ones. But the music from all instruments arrives in cadence independent of distance, so all frequencies must travel at nearly the same speed. Recall that

In a given medium under fixed conditions, v is constant, so there is a relationship between f and λ ; λ ; the higher the frequency, the smaller the wavelength ( Figure 17.10 ).

Example 17.1

Calculating wavelengths.

• Identify knowns. The value for v is given by v = ( 331 m/s ) T 273 K . v = ( 331 m/s ) T 273 K .
• Convert the temperature into kelvins and then enter the temperature into the equation v = ( 331 m/s ) 303 K 273 K = 348.7 m/s . v = ( 331 m/s ) 303 K 273 K = 348.7 m/s .
• Solve the relationship between speed and wavelength for λ : λ = v f . λ = v f .
• Enter the speed and the minimum frequency to give the maximum wavelength: λ max = ​ 348.7 m/s 20 Hz = 17 m . λ max = ​ 348.7 m/s 20 Hz = 17 m .
• Enter the speed and the maximum frequency to give the minimum wavelength: λ min = 348.7 m/s 20,000 Hz = 0.017 m = 1.7 cm . λ min = 348.7 m/s 20,000 Hz = 0.017 m = 1.7 cm .

Significance

The speed of sound can change when sound travels from one medium to another, but the frequency usually remains the same. This is similar to the frequency of a wave on a string being equal to the frequency of the force oscillating the string. If v changes and f remains the same, then the wavelength λ λ must change. That is, because v = f λ v = f λ , the higher the speed of a sound, the greater its wavelength for a given frequency.

Check Your Understanding 17.1

Imagine you observe two firework shells explode. You hear the explosion of one as soon as you see it. However, you see the other shell for several milliseconds before you hear the explosion. Explain why this is so.

Although sound waves in a fluid are longitudinal, sound waves in a solid travel both as longitudinal waves and transverse waves. Seismic waves , which are essentially sound waves in Earth’s crust produced by earthquakes, are an interesting example of how the speed of sound depends on the rigidity of the medium. Earthquakes produce both longitudinal and transverse waves, and these travel at different speeds. The bulk modulus of granite is greater than its shear modulus. For that reason, the speed of longitudinal or pressure waves (P-waves) in earthquakes in granite is significantly higher than the speed of transverse or shear waves (S-waves). Both types of earthquake waves travel slower in less rigid material, such as sediments. P-waves have speeds of 4 to 7 km/s, and S-waves range in speed from 2 to 5 km/s, both being faster in more rigid material. The P-wave gets progressively farther ahead of the S-wave as they travel through Earth’s crust. The time between the P- and S-waves is routinely used to determine the distance to their source, the epicenter of the earthquake. Because S-waves do not pass through the liquid core, two shadow regions are produced ( Figure 17.11 ).

Seismologists and geophysicists use properties and velocities of earthquake waves to study the Earth's interior, which due to it's depth and pressure is not observable through many other means. In fact, the discoveries of the structure of the Earth, illustrated in the figure above, resulted from earthquake observations. In 1914, Beno Gutenberg used differences in wave speeds to determine that there must be a liquid core within the mantle. In 1936, Inge Lehmann began investigating P-waves from a New Zealand earthquake that had unexpectedly reached Europe, which should have been in the shadow region. Up until that point, seismologists had explained such shadow waves as being caused by some type of diffraction (as Gutenberg himself assumed) or a result of faulty seismometers. However, Lehmann had installed the European instruments herself, and so trusted their accuracy. She calculated that the amplitude of the waves must be caused by the existence of a solid inner core within the liquid core. This model has been accepted and reinforced by decades of subsequent calculations, including those from nuclear test explosions, which can be measured very precisely.

As sound waves move away from a speaker, or away from the epicenter of an earthquake, their power per unit area decreases. This is why the sound is very loud near a speaker and becomes less loud as you move away from the speaker. This also explains why there can be an extreme amount of damage at the epicenter of an earthquake but only tremors are felt in areas far from the epicenter. The power per unit area is known as the intensity, and in the next section, we will discuss how the intensity depends on the distance from the source.

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Sound Waves

Part of Science Physics

What are sound waves?

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Sound waves are produced by a vibrating object. Everything that makes a sound must have a part that vibrates.

Engineers show us the key components in a loudspeaker and explain how they work

A two-minute video showing you how to make a speaker from wire, a cup and a magnet.

Sound waves can reflect off surfaces. We hear reflected sound as an echo. Hard, smooth surfaces are particularly good at reflecting sound. This is why large, empty rooms produce lots of echoes.

Soft, rough surfaces are good at absorbing sound. This is why rooms with carpets and curtains do not usually produce lots of echoes. People in a room will help to absorb sound too. The sound made by a band is very different in an empty concert arena than when it is full.

A case study video on how a producer applies the concept of sound waves to their job.

BBC Radio sound engineer Tom Parnell talks about the different microphones and speakers used for recordings at the BBC's MediaCityUK studios in Salford

Our ears have two important functions:

• To collect sounds, convert them to electrical signals and send them to the brain
• To maintain our sense of balance

The ear is made up of three different sections that work together: the outer ear, the middle ear, and the inner ear.

• Parts - pinna and ear canal
• Job - collecting sounds

The eardrum separates the outer ear from the air-filled middle ear. Sound waves make it vibrate.

• Parts - hammer, anvil and stirrup
• Job - to pass vibrations from the eardrum to the inner ear
• Parts - cochlea and semi-circular canals
• Job - to convert the vibrations from the middle ear into nerve signals and to help you balance

A narrow tube called the eustachian tube runs from the middle ear to the back of the nose and makes sure that the pressure is the same on both sides of the eardrum.

When your ears pop the eardrum moves back into place, easing any pressure difference, and making you feel more comfortable. The eustachian tube can open automatically when you swallow, blow your nose or yawn. When you do these motions, you'll often hear a clicking or popping sound.

How we hear:

• a sound wave is funnelled into the ear canal by the pinna
• the vibrations in the air make the eardrum vibrate
• these vibrations are passed through the three small bones (called ossicles) to a spiral structure called the cochlea
• electrical nerve signals are passed from the cochlea to the brain through the auditory nerve
• our brain interprets these signals as sound

The energy changes in the ear are:

How we hear

Properties of sound

The frequency of a sound wave is related to the pitch that is heard:

• a high frequency sound wave has a high pitch;
• a low frequency sound wave has a low pitch.

The amplitude of a sound wave is related to the volume of the sound:

• large amplitude sound waves are loud;
• small amplitude sound waves are quiet.

Amplitude and frequency can be displayed on an oscilloscope connected to a microphone

Oscilloscope traces showing the following sounds:

• Trace 1. small amplitude, low frequency → a quiet, low pitch sound.
• Trace 2. large amplitude, low frequency → a loud, low pitch sound.
• Trace 3. large amplitude, high frequency → a loud, high pitch sound.

Frequency and amplitude

The speed of sound

The speed of sound in air can measured using two wooden blocks, a tape measure or trundle wheel and a stopwatch:

• two people (person A and person B) are placed a distance apart, e.g. 200 m
• person A bangs two wooden blocks together
• person B starts a stopwatch on seeing the blocks bang together and stops the stopwatch on hearing the sound
• the time taken for the sound to travel from A to B is recorded in the table
• repeat the procedure ten times and calculate an average time

The speed of sound can be calculated using the equation:

Speed \( = \frac{{distance,travelled}}{{time,taken}}\)

For example, two people are 200 m apart. The average time for sound to travel the 200 m between them is measured to be 0.59 s

Speed = 200 ÷ 0.59 = 339 m/s

Using microphones and data logger

To measure the speed of sound in the lab, a much more accurate timing method is required because the distance travelled by the sound is much shorter. This can be achieved using a data logger

The data logger can measure and record the time taken for sound to travel between two microphones. Unlike the wooden block method, these can be quite close together.

For example, two microphones are 3.4 m apart. The data logger recorded a time of 0.01 s for the sound to travel between the microphones.

Speed \( = = \frac{{distance,travelled}}{{time,taken}}\)

Speed = 3.4 ÷ 0.01 = 340 m/s

The speed of sound is often taken to be 340m/s in air, but it varies depending on temperature and air pressure. 340 m/s is about 760 miles per hour.

Sound travels faster through liquids and solids than it does through air and other gases. The table gives some examples.

This is because the particles of gases are further apart than liquids or solids. Sound waves travel more slowly when particles are further apart.

Can sound travel through a vacuum?

Sound can travel through solids, liquids and gases, but can it travel through a vacuum?A simple experiment will give us the answer.

Connect an electric bell to a battery and switch. Close the switch and listen to it ring.

Ultrasound has many applications in medicine, including ultrasound scans to check on the health of unborn babies.

Scans of foetuses (unborn babies developing in the womb) are made this way and are used, for example, to measure the diameter of the head of a foetus so that growth can be monitored.

Doctors like using ultrasound images because:

• ultrasound does not harm the patient, mother or foetus in any way
• images of internal organs like the heart can be seen without having to operate on patients
• the equipment is easy to use and relatively cheap

Echo sounding

High frequency ultrasound waves can be used to detect objects in deep water and to measure the depth of the sea. Ultrasound is reflected off an object in the sea or from the seabed, and the echo is detected.

This technique is applied in sonar systems used to measure the depth of the seabed and to find shipwrecks, submarines and shoals of fish. The time between a pulse of sound being transmitted and detected (its echo), and the speed of sound in water are used in the calculation.

SONAR stands for SO und N avigation A nd R anging.

One of the reasons for using ultrasound for sonar is that humans using the water for swimming or diving don’t hear it and so are not disturbed.

Bats and dolphins use a similar method, called echolocation, to detect their surroundings and to find food.

A sonar system on a boat sends an ultrasound pulse towards the seabed.The pulse is reflected, and it is detected 0.16 s later by the system.

Calculate the depth of water if the speed of sound in water is 1 500 m/s.

distance = speed × time

speed = 1 500 m/s

time for ultrasound to travel to seabed and back again = 0.16 s

We are calculating the depth of the seabed, so we only need the time for the ultrasound to travel to the seabed (be careful to remember this part of the calculation)

time for the ultrasound just to travel to the seabed = 0.16 s ÷ 2 = 0.08s

distance to seabed = 1 500 × 0.08 = 120 m

The depth of water is 120 m.

Noise and damage to the ear

We are subjected to sounds pretty much all the time. Many sounds are nice, and we enjoy them. But what is nice to you might not be so nice to somebody else who is also hearing the sound.

Noise is unwanted sound

Heat transfer

• count 5 of 8

Forces, Pressure and Speed

• count 6 of 8

• count 7 of 8

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Traveling waves

17 How sound moves

Speed of sound.

There’s a delay between when a sound is created and when it is heard. In everyday life, the delay is usually too short to notice. However, the delay can be noticeable if the distance between source and detector is large enough. You see lightning before you hear the thunder. If you’ve sat in the outfield seats in a baseball stadium, you’ve experienced the delay between seeing the player hit the ball and the sound of the “whack.” Life experiences tell us that sound travels fast, but not nearly as fast as light does. Careful experiments confirm this idea.

The speed of sound in air is roughly 340 m/s. The actual value depends somewhat on the temperature and humidity. In everyday terms, sound travels about the length of three and a half foot ball fields every second- about 50% faster than a Boeing 747 (roughly 250 m/s). This may seem fast, but it’s tiny compared to light, which travels roughly a million times faster than sound (roughly 300,000,000 m/s).

Sound requires some material in which to propagate (i.e. travel). This material sound travels through is called the medium . You can show that sound requires a medium by putting a cell phone inside a glass jar connected to a vacuum pump. As the air is removed from the jar, the cell phone’s ringer gets quieter and quieter. A youTube video (2:05 min) produced by the UNSW PhysClips project shows the demo with a drumming toy monkey [1] instead of a cell phone.

What affects the speed of sound?

Sound travels at different speeds though different materials. The physical properties of the medium are the only factors that affect the speed of sound- nothing else matters.

The speed of sound in a material is determined mainly by two properties- the stiffness of the material and the density of the material. Sound travels fastest through materials that are stiff and light. In general, sound travels fastest through solids, slower through liquids and slowest through gasses. (See the table on this page). This may seem backwards- after all, metals are quite dense. However, the high density of metals is more than offset by far greater stiffness (compared to liquids and solids).

The speed of sound in air depends mainly on temperature. The speed of sound is 331 m/s in dry air at 0 o Celsius and increases slightly with temperature- about 0.6 m/s for every 1 o Celsius for temperatures commonly found on Earth. Though speed of sound in air also depends on humidity, the effect is tiny- sound travels only about 1 m/s faster in air with 100% humidity air at 20 o C than it does in completely dry air at the same temperature.

Nothing else matters

The properties of the medium are the only factors that affect the speed of sound- nothing else matters.

Frequency of the sound does not matter- high frequency sounds travel at the same speed as low frequency sounds. If you’ve ever listened to music, you’ve witnessed this-  the low notes and the high notes that were made simultaneously reach you simultaneously, even if you are far from the stage. If you’ve heard someone shout from across a field, you’ve noticed that the entire shout sound (which contains many different frequencies at once) reaches you at the same time. If different frequencies traveled at different rates, some frequencies would arrive before others.

The amplitude of the sound does not matter- loud sounds and quiet ones travel at the same speed. Whisper or yell- it doesn’t matter. The sound still takes the same amount of time to reach the listener.  You’ve probably heard that you can figure out how far away the lightning by counting the seconds between when you see lightning and hear thunder. If the speed of sound depended on loudness, this rule of thumb would have to account for loudness- yet there is nothing in the rule about loud vs. quiet thunder. The rule of thumb works the same for all thunder- regardless of loudness . That’s because the speed of sound doesn’t depend on amplitude.

Stop to thinks

• Which takes longer to cross a football field: the sound of a high pitched chirp emitted by a fruit bat or the (relatively) low pitched sound emitted by a trumpet?
• Which sound takes longer to travel 100 meters: the sound of a snapping twig in the forest or the sound of a gunshot?
• Which takes longer to travel the distance of a football field: the low pitched sound of a whale or the somewhat higher pitched sound of a human being?

Constant speed

Sound travels at a constant speed. Sound does not speed up or slow down as it travels (unless the properties of the material the sound is going through changes). I know what you’re thinking- how is that possible? Sounds die out as they travel, right? True. That means sounds must slow down and come to a stop, right? Wrong. As sound travels, its amplitude decreases- but that’s not the same thing as slowing down. Sound (in air) covers roughly 340 meters each and every second, even as its amplitude shrinks. Eventually, the amplitude gets small enough that the sound is undetectable. A sound’s amplitude shrinks as it travels, but its speed remains constant.

The basic equation for constant speed motion (shown below) applies to sound.

[latex]d=vt[/latex]

In this equation, [latex]d[/latex] represents the distance traveled by the sound, [latex]t[/latex] represents the amount of time it took to go that distance and [latex]v[/latex] represents the speed.

Rule of thumb for lightning example

Example: thunder and lightning.

The rule of thumb for figuring out how far away a lightning strike is from you is this:

Count the number of seconds between when you see the lightning and hear the thunder. Divide the number of seconds by five to find out how many miles away the lightning hit.

According to this rule, what is the speed of sound in air? How does the speed of sound implied by this rule compare to 340 m/s?

Identify important physics concept :   This question is about speed of sound.

List known and unknown quantities (with letter names and units):

At first glance, it doesn’t look like there’s enough information to solve the problem. We were asked to find speed, but not given either a time or a distance. However, the problem does allow us to figure out a distance if we know the time- “Divide the number of seconds by five to find out how many miles away the lightning hit.” So, let’s make up a time and see what happens; if the time is 10 seconds, the rule of thumb says that the distance should be 2 miles.

[latex]v= \: ?[/latex]

[latex]d=2 \: miles[/latex]

[latex]t=10 \: seconds[/latex]

You might ask “Is making stuff up OK here?” The answer is YES! If the rule of thumb is right, it should work no matter what time we choose. (To check if the rule is OK, we should probably test it with more than just one distance-time combination, but we’ll assume the rule is OK for now).

Do the algebra:  The equation is already solved for speed. Move on to the next step.

Do unit conversions (if needed) then plug in numbers:  If you just plug in the numbers, the speed comes out in miles per second:

[latex]v = \frac{2 \: miles} {10 \: seconds}=0.2 \: \frac{miles} {second}[/latex]

We are asked to compare this speed to 340 m/s, so a unit conversion is in order; since there are 1609 meters in a mile:

[latex]v =0.2 \: \frac{miles} {second}*\frac{1609 \: meters} {1 \:mile}=320 \frac{m}{s}[/latex]

Reflect on the answer:

• The answer for speed from the rule of thumb is less than 10% off the actual value of roughly 340 m/s- surprisingly close!
• At the beginning, we assumed a time of 10 seconds. Does the result hold up for other choices? A quick check shows that it does! For instance, if we use a time of 5 seconds, the rule of thumb gives a distance of 1 mile, and the math still gives a speed of 0.2 miles/second. The speed will be the same no matter what time we pick. The reason is this:  The more time it takes the thunder to arrive, the farther away the lightning strike is, but the speed remains the same. In the equation for speed, both time and distance change by the same factor and the overall fraction remains unchanged.

Stop to think answers

• Both sounds take the same amount of time. (High and low pitched sounds travel at the same speed).
• Both sounds take the same amount of time. (Quiet sounds and loud sounds travel at the same speed).
• The sound of the whale travels the distance in less time- assuming sound from the whale travels in water and sound from the human travels in air. Sound travels faster in water than in air. (The info about frequency was given just to throw you off- frequency doesn’t matter).
• Wolfe, J. (2014, February 20). Properties of Sound. Retrieved from https://www.youtube.com/watch?v=P8-govgAffY ↵

Understanding Sound Copyright © by dsa2gamba and abbottds is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

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Why Does Sound Travel Faster In Solids? Explained

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The speed at which sound travels varies significantly depending on the material it moves through. (Image: Unsplash)

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FREE K-12 standards-aligned STEM

curriculum for educators everywhere!

Find more at TeachEngineering.org .

• TeachEngineering
• Traveling Sound

Hands-on Activity Traveling Sound

Grade Level: 4 (3-5)

Time Required: 30 minutes

Expendable Cost/Group: US $2.00

Group Size: 2

Activity Dependency: None

Subject Areas: Physical Science, Reasoning and Proof, Science and Technology

NGSS Performance Expectations:

Curriculum in this Unit Units serve as guides to a particular content or subject area. Nested under units are lessons (in purple) and hands-on activities (in blue). Note that not all lessons and activities will exist under a unit, and instead may exist as "standalone" curriculum.

• Seeing and Feeling Sound Vibrations
• Pitch and Frequency
• Sound Visualization Stations

TE Newsletter

Engineering connection, learning objectives, materials list, worksheets and attachments, more curriculum like this, pre-req knowledge, introduction/motivation, vocabulary/definitions, troubleshooting tips, activity extensions, activity scaling, user comments & tips.

Sound and acoustic engineers know that the shape of a room and its materials greatly impact how sound waves travel. Recording studios are designed in soundproof booths so that the recorded music does not contain any unwanted external noise. Libraries are designed to reduce any introduced noises, to assure a quiet, non-distracting learning environment. Concert halls are designed so that sound generated on the stage travels to the back of the space without being distorted.

After this activity, students should be able to:

• Explain that sound can move through solids, liquids and gases.
• Describe how sound needs molecules to move and that changing the medium that it travels through changes the sound.
• Describe how engineers use sound energy when designing spaces, such as movie theaters.

Educational Standards Each TeachEngineering lesson or activity is correlated to one or more K-12 science, technology, engineering or math (STEM) educational standards. All 100,000+ K-12 STEM standards covered in TeachEngineering are collected, maintained and packaged by the Achievement Standards Network (ASN) , a project of D2L (www.achievementstandards.org). In the ASN, standards are hierarchically structured: first by source; e.g. , by state; within source by type; e.g. , science or mathematics; within type by subtype, then by grade, etc .

Ngss: next generation science standards - science, international technology and engineering educators association - technology.

View aligned curriculum

Do you agree with this alignment? Thanks for your feedback!

State Standards

Colorado - science.

Each group needs:

• large bowl (metal works best)
• 2 metal objects, such as spoons, to knock together
• Traveling Sound Worksheet , one per student

A basic understanding of the phases of matter: liquids, solids and gases.

Sound engineers are especially interested in the way sound travels. Can you hear as well when you sit in the back of the class as when you sit in the front? What about in the assembly hall or gymnasium? On the playground? Can you think of other times when you cannot hear as well as someone else? What happened? How about in a movie theater? What do engineers do so that the sound quality is good for everyone in a movie theater? (Possible answers: Add speakers around the room, curtains, carpet the walls, cone-shaped theaters act like a megaphone and help to direct sound waves further.)

Which is louder—walking on carpet or on tile? It is quieter on carpet because the carpet absorbs the sound energy . Sound energy, light energy and other types of energy, need molecules to travel through and vibrate , but sometimes sound energy is absorbed by an object or material. Engineers use this idea when designing rooms that are meant to be quiet. Have you ever noticed how the walls of a movie theater are covered with carpet or fabric? This is to prevent echoing of the sound system. Sometimes when you are in an empty room, your voice echoes or sounds hollow. This is because an empty room has no materials in it that might absorb the sound energy, so the sound bounces off the hard walls, back at you. This makes it hard to hear clearly.

Do you think sound energy can travel through air? Of course it can! That is how sound energy travels when you talk to a friend. How about water? Can you hear sound travel under water? How about a solid? Can sound move through a solid object? Engineers want to know if sound can travel through solids, liquids and gases so they can develop ways to send messages to people all over the world. Can you imagine how great sound would be if it could travel anywhere?

Understanding the properties of sound and how sound waves travel helps engineers determine the best room shape and construction materials when designing libraries, classrooms, sound recording studios, concert halls and theatres. Room shape and materials can impact how sound waves travel since sound waves bounce off different object in different ways. In this activity, we are going to study how sound waves travel through liquids, solids and gases, and think about how engineers might use this information.

Before the Activity

• Gather materials and make copies of the Traveling Sound Worksheet .
• Divide the class into teams of two students each.

With the Students

• Ask the students to predict if sound can move through solids, liquids and gases.
• Have the students complete the worksheet, which leads them through traveling sound wave activities.
• Can sound energy travel through solids? Students place their ears on a desk or table as they tap or scratch on the top. They compare that to the same sound made when their ear is not pressed to the table.
• Can sound energy traveling through liquids? Fill a large bowl or bucket (metal works best) with water. One student taps two spoons together under the water. Two other students observe and compare the tapping sound they hear, as heard through the air and as heard by placing an ear against the bowl.
• Can sound energy traveling through gases (air)? The students feel their throats gently during each of these tasks:
• Hum with your mouth and nose open.
• Hum with your mouth open and nose closed.
• Hum with your mouth closed and nose open.
• Hum with your mouth and nose closed.
• Discuss with the students what happened. Were their predictions correct? Can sound travel through air, water and solids? (Answer: Yes!) Sound needs molecules to move. Solids, liquids and gases are all made of molecules. The characteristics of the molecules (for example, the space between the molecules) determine whether the sound becomes muffled or changes in some way.
• How might engineers use the knowledge that sound travels through solids, liquids and gases? (Possible answers: Engineers create devices that send sound anywhere — through water to a submarine in the ocean, through wires to your TV, and through the air in surround sound movie theaters or emergency broadcast signals.)

echo: Repetition of a sound by reflection of sound waves from a surface.

frequency: The rate of vibrations in different pitches.

pitch: The highness or lowness of a sound.

sound energy: Audible energy that is released when you talk, play musical instruments or slam a door.

sound wave: A longitudinal pressure wave of audible or inaudible sound.

vibration: When something moves back and forth, it is said to vibrate. Sound is made by vibrations that are usually too fast to see.

volume: When sound becomes louder or softer.

wave: A disturbance that travels through a medium, such as air or water.

Pre-Activity Assessment

Prediction: Ask students if they think sound can move through solid, liquid, and gas. If so what are some examples? (Possible examples: Students may recall talking under water or using tin can and string telephones.)

Activity Embedded Assessment

Worksheet: Have students use the Traveling Sounds Worksheet to guide them in the activity and as a place to record their observations. Review their answers to gauge their mastery of the subject.

Post-Activity Assessment

Toss-a-Question:  Ask students to independently think of an answer to the question below and write it on a half sheet of paper. Have students wad up and toss the paper to another team member who then adds their answer idea. After all students have written down ideas, have them toss the paper wad to another team, who reads the answers aloud to the class. Discuss answers with the class.

• What is an example of something through which sound can travel?

Neighbor Check: Have the students compare their activity observations with a neighbor. Are they the same or different? Have each team report some of their similar and dissimilar observations to the rest of the class.

Engineering Design: The supply of air on Earth is running out! Several futuristic cities for human habitation are being designed either underwater or deep inside mountains. Have each student group become a city planning engineering team and draw a communication system for sending emergency messages between the new cities. Make sure to illustrate and describe how the sound energy (message) will move through air, water or solid rock.

This activity can be very loud. Ask students to not disturb others while they learn and have fun.

To bring some humor to the activity, ask each student to hum a small part of their favorite song while feeling their throat. Have each student alternate between having their nose and mouth open or closed while humming non-stop. Why does the sound change depending on whether you close your nose or mouth? What happens if you block your ears? What does this activity teach us about sound? (Answer: Sound vibrations must travel through air for us to hear them. Like a musical instrument [perhaps a recorder or flute], if you change the holes where sound escapes, it changes the pitch, but not the frequency/vibrations of the sound.)

If a metal bowl is used during the activity, the vibrations from the objects colliding underwater vibrate the bowl, creating the illusion that the bowl is being struck. Have students draw the vibrations in the bowl on a piece of paper. Do the vibrations change if the objects are tapped together increasing softly?

Have students think about different forms of communications. Does sound travel most often through solids, liquids or gases? Have students poll their friends, family and neighbors to solicit their ideas.

For lower grades, conduct the activities as a class instead of in teams. Younger students could also draw pictures of their observations instead of writing in sentence form.

Students are introduced to the sound environment as an important aspect of a room or building. Several examples of acoustical engineering design for varied environments are presented.

Students learn how different materials reflect and absorb sound.

Students learn that sound is energy and has the ability to do work. Students discover that sound is produced by a vibration and they observe soundwaves and how they travel through mediums. They understand that sound can be absorbed, reflected or transmitted.

Students use the engineering design process to design and create soundproof rooms that use only one type of material. They learn and explore about how these different materials react to sound by absorbing or reflecting sound and then test their theories using a box as a proxy for a soundproof room. ...

Dictionary.com. Lexico Publishing Group, LLC. Accessed December 19, 2005. (Source of some vocabulary definitions, with some adaptation.) http://www.dictionary.com

Contributors

Supporting program, acknowledgements.

The contents of this digital library curriculum were developed under grants from the Fund for the Improvement of Postsecondary Education (FIPSE), U.S. Department of Education and National Science Foundation (GK-12 grant no. 0338326). However, these contents do not necessarily represent the policies of the Department of Education or National Science Foundation, and you should not assume endorsement by the federal government.

Last modified: March 17, 2021

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• Russian Kitchen

The Russian vuvuzela: What noisy instrument will 2018 World Cup fans use?

The spoons deployed in this Russian folk instrument are just that - real spoons, which in Ancient Rus' were part of a dining set.

Russia is preparing for the World Cup. With two years to go, the national instrument fans will play has already been chosen: Wooden spoons, which are a percussion instrument from Ancient Rus'.

Unlike the South African vuvuzela, whose sound was similar to the din of a busy beehive, the Russian spoons have a particular appeal. In expert hands spoons can produce interesting combinations of rhythmical sounds, which in a way resemble those of Spanish castanets. But if there are many spoons and it is impossible to maintain a steady rhythm, one thing can still be said: The sound will be very, very loud.

The spoons deployed in this Russian folk instrument are just that - real spoons, which in Ancient Rus' were part of a dining set. They were made of various types of wood, including linden, aspen, maple and ash. It is not known precisely when the spoons were first used as musical instruments. The first citation is from the 13th century but some historians give a date for first use in the late 18th century.

The difference between them and the spoons used for eating is in their durability. To strengthen them, they are mostly made of thick and hard wood, such as maple or birch. The type of timber also determines the timbre of sound produced.

One of the main requirements that a World Cup fan's national musical instrument must meet is its cultural association with the host country. Russia has a long list of national instruments, but the spoons came out top.

"From the beginning we excluded wind instruments due to the large-scale criticism of the vuvuzela used in South Africa. Then we excluded bulky instruments that are difficult to use, such as the balalaika, the accordion, as well as string instruments like the gusli [a type of lyre], but also the horn, the cymbals and others," Rustam Nugmanov told  (in Russian) Znak.com. A musical instrument maker from Moscow's Elektrostal suburb, he came up with the idea to make the spoons a symbol of the 2018 World Cup in Russia.

The idea came to him in 2010 when in Zurich Russia officially announced its intention to host the championship. But obviously he could not propose using those spoons that Russians are familiar with.

Better bowls

The quantity of spoons that are held varies depending on the complexity of the rhythm and deftness of the spoon player. However, novices will have a hard time even with the basic number (two pieces) since the spoons must skillfully be placed between the fingers. Even Russians do not do a good job in the beginning. Especially since very few people play spoons - today the instrument can only be found in souvenir stands and is bought mostly by tourists who are unlikely to understand all its possibilities.

Whatever the case, spoons are not the mainstream - they are used only by Russian folk ensembles. And they are not pipes, with which to create a noise you just have to blow into them.

Nugmanov considered this problem. He developed a rubber fixer - a V-shaped holder, which will help circumvent long training sessions to master the instrument. Thanks to the fixer, the instrument now resembles the Latin letter V, alluding to the word Victoria, which means victory in Latin. The instrument's working title for now is "spoons of victory."

Russian President Vladimir Putin has already approved the idea and Nugmanov expects to receive a presidential grant of about one million rubles ($17,000). Industrial designers and planners will be invited to work on the "spoons of victory" project. Also, "a series of scientific and sociological studies" will be conducted (apparently, to make sure no one goes crazy).

Read more: How horsehair, sheep's wool and soft stone became objets d'art in Tuva>>>

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The Sounds of Moscow

Travelling is not a mono-sensory experience. This thought has always been there, lurking at the back of my head throughout my early wanderings. I only became fully aware of it, though, when I embarked on a long journey with a friend of mine, who happens to be blind. We went down the Transsiberian track together and she drew my attention to many things I would have otherwise taken for granted: the sound of crackling snow, the voices of people arguing at markets, the trashy pop playing on the minibus from Irkutsk to the shores of Lake Baikal (well, okay, I probably would have noticed this one anyways), the smells I would have probably registered, but had never associated with anything I knew.

When I moved to Moscow some time later, I caught myself paying close attention to all the sounds, as if trying to convey the ambiance of this new place to my favourite travel companion. This made me realise how important they were for my perception of Moscow as a whole. Moscow does look different from any other place I’ve been to; it’s majestic Stalinist baroque interwoven with the pragmatism of the 70s and the showoff ambitions of the early 2000s make for quite a unique combination. It doesn’t only look different, though, it sounds different — and I had not known that before coming. I have read hundreds of pages about Russia in general and Moscow in particular, and I have seen plenty of online publications about them. None of those gave me any hint about what Moscow might sound like. To fill this gap, I started sending Sound Postcards: small recordings of sounds that, piled together, make Moscow what it is to me. Here is a small selection of those:

You cannot overestimate the importance of the metro. I don’t know what role the underground plays in London or Paris, but in Moscow it is the thread from which the city is woven. The trains are incredibly loud. It makes it impossible to talk; it’s impossible to think there either. The unbearable roar follows a monotonous, repetitive pattern of high and low pitch, speeding up and slowing down, broken by announcements of station names and general reminders of good manners. This pattern changes abruptly when a train happens to peep outside the tunnel for a moment. The sound, previously crammed into the narrow space, spreads across the entire width of the Moskva River, making the train feel peacefully quiet. This contrast is soothing in a way no words can describe. At the very beginning of my stay there I would hear it every time I was going home, between Avtozavodskaya and Kolomenskaya. The tunnel there ended unexpectedly and the change was particularly well audible (or so I hoped):

The metro is like Moscow itself: there are stations the sole goal of which is to impress and intimidate, and there are the mundane, pragmatic ones, scattered outside the centre, aimed simply at delivering the locals all the way to work and back. The former are just the export face of Moscow and, by extension, of Russia as a whole: a huge Potemkin village to hide the country and its problems. The latter are what real, everyday Moscow is like: they witness the early morning commute, coming home late at night and the permanent deficit of time. Needless to say, these are the latter which draw my particular interest. They are their own microcosms extending their halo many streets away from the actual station. Far from the centre, the stations are also the hubs of cultural and economic activity. At night they are the starting points for the exploration of Moscow’s nightlife. In the afternoons, though, they become impromptu markets selling anything from fresh vegetables through bus tickets to pepper spray. This is what they sound like:

Moscow can be ruthless, and whatever you choose to do here, you can be sure that there’s already someone else doing the exact same thing, and probably doing it better. The competition is very high, so businesses need to find ways to stand out. One of them is hiring people to hand out leaflets and shout catchy slogans near the entrances to the metro stations. I will forever remember the squeaky ‘Iuristy, advokaty, bezplatnye konsutlacii’ I have heard a million times near Sulkharyevskaya. One stressful evening, while flat hunting near Elektrozavodskaya, I heard this lady, who is by far the most devoted, not to say desperate, street vendor I have heard in my entire life:

Certain metro stations are way busier than others. Kurskaya is very close to the top of that ranking: three metro lines and a big train station all intersect here. Thousands of people pass through it every day. It’s no surprise then that its central vestibule draws plenty of street performers. The one you can hear below is, by far, the most interesting one I’ve heard there. I still don’t know what instrument he was playing, but I don’t mind it any more. It only adds to the air of mystery this piece evokes in me.

When it comes to street performers, Moscow can showcase quite a unique selection. They appear wherever there are people, and given the degree of competition, they reach the heights of their creativity to stand out. My favourite one, though, doesn’t need to do that. He just shows up and sings — and that is more than enough. He is an elderly, elderly man, who sets up his accordion stand right next to 1905 Goda metro station. He has two chairs: he sits on one and puts his multiple belongings on the other. He has a microphone, a little speaker and a songbook, and he sings cheerful songs about being young, falling in love, going to war and coming back victorious. He does everything slowly and meticulously, and he never stops until whatever he’s doing is completed. He’s an unlikely role model I found one evening on my way back from work.

Russians love poetry. It’s a part of popular culture here to an extent I have not seen anywhere else. It makes its way out of school and into the everyday conversations, parties in the kitchen, TV shows. It also has its place among the street performers. One day, on my way from the Red Square to Lubyanka, I heard this man, reciting what I believe to be Yesenin’s poetry:

Moscow is a melting pot of cultures: western influences get mixed up here with Russian culture, but also with the habits and traditions brought by incoming migrants from central Asia and Russia’s far east. Given the Western media narrative about Russia, it is easy to overlook how diverse it is. There are dozens of different religious and ethnic groups living east of Moscow, as close as Kazan and as far as Vladivostok – and everywhere in between. I got a tiny sample of it one very late evening, walking past the outer wall of the Historical Museum, right outside Red Square. Those two ladies, wearing as much of their national outfits as the weather would permit, were singing beautifully in a language which definitely wasn’t Russian. I can only guess what they were singing about, but I want to believe they were praising the beauty of the Russian steppes and the freedom they can give.

Music, just like poetry, is of vital importance in everyday life. Russians sing a lot. At an open mic in an expat bar I used to go to, after the obligatory hours of extremely talented (and sometimes not-that-talented) performers covering various hits of the Anglo-Saxon tradition, the Russian organiser of the event would take over the microphone and sing a couple of Russian ’80s rock songs. The change of atmosphere in the room was instantaneous, almost physically visible, yet it remains extremely difficult to close it in a simple description. All the Russians present in the room would sing along from the very beginning till the very end. It felt as if they shared one experience, as if they understood each other without words, as if they were a part of a secret society and the song was a sign by which they recognised each other.

It is difficult to argue what came first: the chicken or the egg, but the fact remains that the Orthodox liturgy is centred around music and that for centuries before the Revolution the Orthodox Church played a huge role in society (after 80 years of persecution its influence is now being rebuilt). The priests and the choir sing in Old Church Slavonic, making the service impossible to understand, yet completely entrancing. Below you can hear a liturgy in the Cathedral of Christ the Saviour which I stumbled upon one early winter morning on my way to work.

It wasn’t a holiday I had been aware of. It was a weekday, early in the morning. As I was walking to work, I saw big screens set up in front of the church. On my way back, an hour and a half later, I heard these bells calling the faithful to prayer. A crowd of people, unusual for the still early hour, were flowing towards the church. I followed the bells and the people and heard the service you have just heard as well.

All of the sounds above — and many more, hidden well in the corners of multiple memory cards, waiting to be discovered — make up Moscow as I know it. They are just as important to me as the towers of the Kremlin and St. Basil’s Cathedral from all the postcards. Who knows, maybe, having listened to all of these, you’ll suddenly start noticing the extraordinary sounds around you? Please, do — they are definitely worth the while.