# Explain why speed of sound changes in different media.

1. Dec 7, 2009

### chown

1. The problem statement, all variables and given/known data
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?

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

3. 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.

Last edited: Dec 7, 2009
2. Dec 7, 2009

### denverdoc

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.

3. Dec 7, 2009

### chown

What about the medium causes the wavelength to decrease?

4. Dec 7, 2009

### denverdoc

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.

5. Dec 7, 2009

### denverdoc

Well lets 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.

6. Dec 7, 2009

### chown

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

7. Dec 7, 2009

### denverdoc

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?

8. Dec 7, 2009

### denverdoc

The other question--is why c varies. You mentioned a couple. But lets 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.

9. Dec 7, 2009

### chown

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.

10. Dec 7, 2009

### denverdoc

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).

11. Dec 7, 2009

### AEM

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.

Last edited: Dec 7, 2009
12. Dec 7, 2009

### denverdoc

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

13. Dec 7, 2009

### ideasrule

Um, there's no sound in space.

14. Dec 7, 2009

### denverdoc

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.

15. Dec 8, 2009

### ideasrule

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.

16. Dec 8, 2009

### AEM

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 :rofl: }

17. Dec 10, 2009

### denverdoc

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.

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