# Explain why speed of sound changes in different media.

• chown
In summary, the characteristics of sound, such as frequency and wavelength, change for the speed of sound to change in each medium. This is because different physical properties of the medium, such as density and elastic properties, affect the speed at which sound travels. For example, when pouring water into a tube, the pitch of the sound increases as more water is poured in due to changes in the medium's properties and the reflections of the sound waves off the water surface. Overall, the speed of sound is dependent on the medium's ability to transmit and propagate a force, similar to how a rumor spreads faster in a densely populated and responsive community.
chown

## Homework Statement

What characteristics of a sound (such as frequency and wavelength) change for the speed of sound to change in each medium? Why do these characteristics change?
For example:
Why does the pitch of sound produced by pouring water into a tube increase as more water is poured in?

## Homework Equations

V = frequency X wavelength
Physical properties of the medium: density, elastic properties, etc.

## The Attempt at a Solution

I understand that sound often travels fastest (out of solids, liquids and gases) in solids, less fast in liquids, and slowest in gases. I understand that the length of the tube changes the standing wave in the tube, but I ponder why the sound speed increase in the water changes the characteristics of the sound (i.e. frequency and/or wavelength). Reflection of the sound wave off of the water surface makes sense. Perhaps some of the sound enters and propagates through the water, then reflects off the bottom of the tube, and exits the water with a different frequency. Perhaps it is the cohesion between the H2O molecules to be a distance apart, where the sound wave energy diffracts around the molecules to create a larger frequency or wavelength.

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What about talking after inhaling Helium. The frequency is the same--dictated by the rate of vocal cord vibration. But the sound is a lot squeakier. Not sure what the explanation is--thought I did bbut removed it after thinking about it more.

What about the medium causes the wavelength to decrease?

Sorry for the dbl post, but it also occurs to me that C=lambda*f so one of the two parameters must change. Frequency is a mechanical event--wavelength can depend on other factors, e.g. the doppler effect.

chown said:
What about the medium causes the wavelength to decrease?

Well let's think about this some. I'm making this up as I go, but it is an interesting question, so indulge me. What is it that determines the wavelength. I still hold that frequency is the fundamental constant in this discussion.

Lets take the positive pulse of a pressure pulse: the speed of sound in the material will dictate how far that positive pressure wave travels. The same argument holds for the reverse part of the cycle: hence wavelength must change.

What about the medium causes the speed of sound to change?

chown said:
What about the medium causes the speed of sound to change?

Lets try this again. Assume you are going to push on the end of a beam for a second and then abruptly switch to pulling on it. The effects of this push/pull will be felt downstream.

How far does the effect of the push get in one second? This is the speed of sound. If C is 50 m/s the push gets 50 meters away before switching to a pull. Likewise the pull gets 50 m before another switch. The sum of the distances is a wavelength. Compare to a situation where C is 5 m/s. What are the differences in wavelength?

The other question--is why c varies. You mentioned a couple. But let's change this to word of mouth--say a rumor gets started--how fast does it spread? Would you rather have a few people or many? Would you rather have a bunch of lazy people who take their time to get things done, or those who get right on it? Answer these right and you have the essentials.

denverdoc said:
Lets try this again. Assume you are going to push on the end of a beam for a second and then abruptly switch to pulling on it. The effects of this push/pull will be felt downstream.

How far does the effect of the push get in one second? This is the speed of sound. If C is 50 m/s the push gets 50 meters away before switching to a pull. Likewise the pull gets 50 m before another switch. The sum of the distances is a wavelength. Compare to a situation where C is 5 m/s. What are the differences in wavelength?

The second wavelength is 1/10 of the first wavelength. But my question is what properties of the beam and pulling system cause the speed to change? In the case of the water, what properties of the water cause the speed to change? Perhaps it is the cohesion between the H2O molecules to be a distance apart, where the sound wave energy diffracts around the molecules to create a larger frequency or wavelength.

chown said:
The second wavelength is 1/10 of the first wavelength. But my question is what properties of the beam and pulling system cause the speed to change? In the case of the water, what properties of the water cause the speed to change? Perhaps it is the cohesion between the H2O molecules to be a distance apart, where the sound wave energy diffracts around the molecules to create a larger frequency or wavelength.

Forget about diffraction for a minute. Reread the last post--speed of sound and wavelength is all about the communication of a force in a sloppy medium. So how do you get a rumor to spread faster? Talk to lots of people (density of material) and those that act on the information fastest (opposite of elasticity).

chown said:

## Homework Statement

What characteristics of a sound (such as frequency and wavelength) change for the speed of sound to change in each medium? Why do these characteristics change?
For example:
Why does the pitch of sound produced by pouring water into a tube increase as more water is poured in?

## Homework Equations

V = frequency X wavelength
Physical properties of the medium: density, elastic properties, etc.

## The Attempt at a Solution

I understand that sound often travels fastest (out of solids, liquids and gases) in solids, less fast in liquids, and slowest in gases. I understand that the length of the tube changes the standing wave in the tube, but I ponder that the sound speed increase in the water changes the characteristics of the sound (i.e. frequency and/or wavelength). Reflection of the sound wave off of the water surface makes sense. Perhaps some of the sound enters and propagates through the water, then reflects off the bottom of the tube, and exits the water with a different frequency.

A rather old reference is "Theoretical Acoustics' by Morse and Ingard. They point out that the velocity of propagation of sound waves in a fluid is

$$\frac{1}{\sqrt{\kappa \rho}}$$

where $$\kappa$$ is the compressibility and $$\rho$$ is the density.

I suspect that the pitch of the sound produced by pouring water into a tube arises because of the shortening of the air column in the tube.

Reflection of sound off of an air/water interface is an example of a general phenomena: the reflection of wave motion when there is a change in the impedance properties of the medium the wave is traveling through. This is why camera lenses are coated. The coating acts as an "impedance matching" device. The human ear has an elaborate mechanical mechanism (the hammer, anvil, and stirrup arrangement) to reduce loss of sound energy between the surrounding air and the fluid in the cochlea.

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Which helps to explain why the speed of sound in space is infinite.

denverdoc said:
Which helps to explain why the speed of sound in space is infinite.

Um, there's no sound in space.

Yes I'm aware of this. Which helps to explain why w/o nearby matter, conduction doesn't occur. The k in the above eqn is misrepresented--it is described as compressibilty when in fact it is is the reciprocal.

denverdoc said:
Yes I'm aware of this. Which helps to explain why w/o nearby matter, conduction doesn't occur. The k in the above eqn is misrepresented--it is described as compressibilty when in fact it is is the reciprocal.

k IS compressibility. Think about it: does sound travel faster in a stiff material, or in a soft, easily compressible one? If you'd like to claim that sound travels faster in an easily compressible material, please find a source.

denverdoc said:
Yes I'm aware of this. Which helps to explain why w/o nearby matter, conduction doesn't occur. The k in the above eqn is misrepresented--it is described as compressibilty when in fact it is is the reciprocal.

The danger in using old references as I did by citing Morse and Ingard is that conventions (fashions) change in physics as they do elsewhere. They define compressibility as

$$\kappa = - \frac {1}{V} ( \frac{ \partial V }{ \partial P } )$$

at constant temperature. This is, of course, the reciprocal of the bulk modulus. So I probably should have written

$$c = \sqrt{ \frac { \beta }{ \rho}}$$

where $$\beta$$ is the bulk modulus.

{ Parenthetical note I'm aghast to see that to get a zero velocity for sound in empty space we must postulate that Morse and Ingard's compressibilty for empty space must be infinite. Shades of the old ether theory for the propagation of light }

Thanks for the clarification, I looked at the original equation and know that density and stiffness woork together, which is why I questioned the term "compressibility" which to me sounds like compliance. I think we are in all agreement that both stiffness and density increase C.

## 1. How does the density of a material affect the speed of sound?

The speed of sound is directly related to the density of a material. In general, the denser the material, the faster sound will travel through it. This is because denser materials have more molecules per unit of volume, allowing sound waves to travel more quickly.

## 2. Why does the speed of sound vary in different media?

The speed of sound varies in different media because each material has a unique molecular structure and density, which affects the way sound waves travel through it. For example, sound travels faster through solids than through liquids or gases due to the closer proximity of molecules in a solid material.

## 3. How does temperature affect the speed of sound?

Temperature has a significant impact on the speed of sound in a material. In general, as the temperature of a material increases, the speed of sound also increases. This is because at higher temperatures, molecules have more kinetic energy and can vibrate more quickly, allowing sound waves to travel faster.

## 4. What role does elasticity play in the speed of sound?

Elasticity, or a material's ability to bounce back to its original shape after being deformed, also affects the speed of sound. In more elastic materials, sound waves can travel faster because the molecules are able to vibrate more quickly and transmit the sound energy more efficiently.

## 5. Can the speed of sound be affected by external factors?

Yes, the speed of sound can be affected by external factors such as air pressure and humidity. For example, sound travels faster in higher air pressure and lower humidity environments due to the increased density of the air. Additionally, wind can also impact the speed of sound by either helping or hindering the propagation of sound waves.

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