# Speed of an air molecule when transmitting sound of frequency f

1. Jul 5, 2009

### luckis11

The speed of sound in the air is constant no matter what its frequency f is. Fine. But what is the speed of an air molecule which transmits that sound of frequency f? The higher the frequency, the higher the speed of the molecule, right? What is the equation which gives this velocity? (and a couple of arithmetical examples).

Last edited: Jul 5, 2009
2. Jul 5, 2009

### negitron

The net velocity is zero.

3. Jul 5, 2009

### diazona

Not really. Sound waves are pressure/density waves, and it takes a really large number of molecules to have a meaningful pressure or density. So the speeds of individual air molecules carrying sound waves are pretty much irrelevant; only the average properties of those large numbers of molecules matter.

4. Jul 5, 2009

### luckis11

If you don't know the answer you'd better not fill the thread with nonsense.

5. Jul 6, 2009

### luckis11

According to some equations I have seen, the speed of the molecule is not constant. So I want its average velocity of which its Δx and Δt are defined by two successive collisions of the molecule with its neighbour molecules.

See how the sound waves are produced by the collisions of each molecule with its neighbour molecules:http://www.surendranath.org/Applets/Waves/Lwave01/Lwave01Applet.html [Broken]
Each molecule corresponds to one moving dot of that simulation.
Set the "frequency" botton at a higher frequency, and you will see that the average speed I am asking for, increases as the frequency increases. However that simulation might not be accurate for this case, because the speed of each wavefront seems to increase as the frequency increases, whereas in the case of sound waves in the air is the same no matter what the frequency is. But what is the cause of a higher frequency? It must be that the molecules are running faster, or else what causes it? Besides, the higher the frequency, the higher the energy and pressure of each wave (although this might not proove the higher speed of the molecules).
That simulation is also confusing, as the problem has the extra complication that the average speed of ALL the molecules of the air is defined by the temperature, which implies that their speed does not increase as the frequency increases (since the temperature remains the same irrespective of the frequency) , but this conclusion might be wrong because not all molecules transmit the sound wave. And we are referring to the molecules which by definition, their motions and collisions cause the particular sound wave. The more molecules transmit it the higher the intensity?

So, I want the equation which gives that average velocity, in relation to the frequency.

Do not quote my posts, as I usually edit them correcting my mistakes. Correct my misconceptions if any, without quoting, unless if necessary.

Last edited by a moderator: May 4, 2017
6. Jul 6, 2009

### Nick Bruno

id suggest lookin thru a heat transfer book. may find something interesting there...
at least with the MFP or mean free path?.. just a suggestion.

7. Jul 6, 2009

### luckis11

The molecule goes back and forth f times in 1 sec, traversing at each of these f times a distance equal to 2A (where A the amplitude), as it traverses twice the amplitude A if every period T, and f=1/T.
So (in order to find the average speed in relation to the f), I only need to find the equation which gives the A in relation to the f.

correct?

To add to the confusion, it seems they have given two different meanings for the term amplitute: I am refererring to the meaning of the distance, the displacement of the molecule between two succesive collisions.

Last edited: Jul 6, 2009
8. Jul 6, 2009

9. Jul 6, 2009

### negitron

There is no definite relationship betwen amplitude and period (or frequency).

10. Jul 6, 2009

### AIR&SPACE

Sorry, started my last post before this was up.

Let me see if I understand you. You want the magnitude of the energy of the molecule.

I say that because if we assume ideal gas, the collisions take zero time to occur. There is no acceleration/deceleration period. If we could graph the velocities it would be non-differentiable. It would look like abs(x) @x=0. And I don't believe there is any negligible energy loss between interactions. There should be radiation energy-loss occurring but that's the negligible loss occurring.

So since the energy transfer is equal, the particle is given a velocity (based on it's mass) instantaneously. This velocity should stay the same until the next interaction.

Now then, tell me if I've got this next part right. YOU want to know if there is a correlation between the energy of the particle between interactions and the frequency of the sound. Correct?

11. Jul 6, 2009

### Lok

Usually the average speed of gas molecules is close to the speed of sound in that medium.

Even though there is no apparent movement while sound gets transmitted, there is an increase in speed followed by a decease inside the wavefront. It is necessary or no information ( momentum, energy, sound) will be transmitted.

The individual molecules travel faster with the increase of freqency but only locally, the speed of sound (of the wavefront) remains the same for the whole sound range.

12. Jul 7, 2009

### luckis11

The amplitude A (the distance in which the molecule is moving), does not depend at all on the frequency and thus does not depend at all on the wavelength λ? And reversly, λ does not depend at all on A? How can this be? Then what causes the different frequencies-wavenengths? Only the speed of the molecules no matter how much the A is? And the A can be however small or large without this affecting how much the λ is?

c=λf, thus λ depends on f. Thus if A does not depend on f, it does not depend on λ either.

Last edited: Jul 7, 2009
13. Jul 7, 2009

### Staff: Mentor

No, not correct. You are confusing amplitude and wavelength. If what you were suggesting were true, then every sound wave of a certain frequency would have the same amplitude. Turning up the volume on your stereo will show you that that isn't true. And if the speaker driver doesn't have a cover, you can actually see its amplitude change as you turn up the volume. Perhaps more to the point, the speed of that speaker driver is well below the speed of sound. If it wasn't, it would destroy the wave it was trying to create.

Amplitude in a sound wave is not measured in units of distance, it is measured in units of pressure.

Your initial question was what is the speed of an air molecule when transmitting sound and that question was answered correctly as the speed of sound. But you also said this:
What equations? Where? What you are trying to describe and saying you have seen - if it existed - would already have given you the answer you were looking for!

What causes frequency? The frequency of a sound wave is the frequency of oscillation of the driver. It's cause has nothing to do with the speed of the molecules or the their amplitude.

Longitudinal waves are tricky this way, so maybe it would help to read up on them some more: http://en.wikipedia.org/wiki/Longitudinal_wave

14. Jul 7, 2009

### luckis11

At page 539 of the "university physics by Hugh Young", at drawing No 19-5, regarding longitudinal waves, it is stating clearly that the amplitude A is the distance in which "the particle" is moving from its equilibrium position till one of the two edges of its displacement. I.e. it travels back and forth within a distance equal to 2A. And in that drawing 19-5, the speaker is also vibrating within a distance equal to 2A. And this 2A, IS NOT the wavelength λ, which is the distance between two successive wavefronts. In that drawing 19-5, the distance λ is greater than the distance 2A. Also, the definition of amplitude in a "harmonic oscillation" is also defined as the above dispacement of the moving object, thus the moving object also corresponds to an air molecule. Each molecule is regarded as not moving with constand speed but accorsing to the harmonic equation equations. I have a small doubt that they might refer to the motion of each wavefront, although all the above clues suggest that they are referring to each molecule. Indeed, even the vibration of the atomic nucleuses within each molecule, are regarded as moving according to harmonic oscillation.

I now see that the molecule traverses a distance equal to 4A (and not 2A), f times in each sec. Thus its average speed is 4Af/sec (sorry, f has already the sec in its denominator thus it's 4Af). Why is this wrong?

I doubt that the speed of sound equals to the speed of each air molecule which transmits this sound, for reasons some of which I mentioned. For example, in that simulation, the speed of the circles increases as f increases. But I repeat that this simulation might be misleading, as the speed of the first wavefront (which is the speed of sound) increases as the f increases, whereas the speed of sound remains the same as the f increases.

You are correct that frequency does not depend on the maximum distance that the speaker is traversing. Thus the distance of the speaker in that drawing 19-5 refers to another vibration of the speaker. So it seems that amplitude has two different definitions. So I am referring to the definition I mentioned, which however, does not identify with the wavelength λ. But wtf, the wave equations have the same symbol A for both of these two definitions? Hm, the two A's might identify. If they identify, then the A does not depend on f, and thus it does not depend on λ either, so...?

The more loud the sound, the greater the distance the speaker is traversing. This also does not affect the speed of the molecules? And no matter how loud the sound, its speed remains constant. If it doesn't affect the speed of each molecule, then how does the pressure and energy of the wave increase? Because (and only because) the number of the molecules which transmit the sound increases? Or only because the number of molecules concentrated in each wavefront increases?

Here's an important clue: Before we switch on the speaker, the air molecules were colliding with the average speed defined by the air temperature. So after we switch on the speaker, we have collisions of the molecules of the speaker with the molecules of the air. So we have a significant change of the speed of the air molecules which transmit and cause the sound, to the direction of the sound, as each air molecule exchanges velocity with its neighbour molecule? Or this change is insignificant? But the simulation at the link I gave above, shows that the waves were produced exactly because there was a change in the speed of the molecules, because of their collision with the speaker, as they were still before that.

An equation which refers to harmonic oscilation says that the maximum speed (of the moving particle) is ωΑ=2πfA. This indicates that the speed of each molecule increases as the frequency f increases, but is this conclusion correct, and also correct regarding the average speed I am asking for?

Anyways, it seems that 4Af is correct, but the question is, does that A decrease as f increases? If yes, it decreases that much so that the speed of the molecule does not increase as the f increases? But then, A does depend on λ and f, so the loundness of the sound defines λ and f? Or the two A's do not identify... here we go again. ARE A AND λ RELATED OR NOT AND IF YES HOW? In the wave equations they are related, but there are extra variables in there (x, y, and/or t) which I must get rid off.

Last edited: Jul 7, 2009
15. Jul 8, 2009

### vin300

Amplitude is the maximum distance a particle in the wave travels from its mean position and does not affect any of wavelength, frequency or velocity. The only difference it makes is in the intensity given by
I=2(pie)^2A^2df^2v
The frequency is the number of times the particle oscillates between two extremes of its amplitude so it need not make a difference in the amplitude.Wavelength is the distance between two particles in phase.
If according to these considerations you are able to represent a transvese wave as longitudinal or vice-versa it makes no difference except that the particle vibrations in a longitudinal wave are exactly in and opposite to the direction of wave propogation while in a transverse wave are both in the direction of the wave and perpendicular.

16. Jul 8, 2009

### luckis11

Have you got a link showing that A and λ do not depend at all on each other?

17. Jul 8, 2009

### vin300

First speak about the equation relating A and lambda

18. Jul 8, 2009

### vin300

Plain right. If the amplitude is zero, then there is no wave because it is a basic property of any wave.
You mentioned it is 4A(and not 2A). This is because the particle travels from mean to the positive extremity, reverse, mean to the negative extremity and reverse back to the mean, each constituting 1/4 of one complete oscillation, because after this, the particle travels from mean to the pos...(cycle repeated). after vibrating a length of 4A and changing its starting mean position to a distance equal to lambda, the particle vibrates in the same phase again(same manner, same velocity).
Next,they are basically vibrations, so they do not have a constant velocity but follow the oscillatory displacement equation:
x=Asin(omega*time + phase constant)

Last edited by a moderator: Jul 10, 2009
19. Jul 10, 2009

### luckis11

Yes, but there is the extra variable x in the last equation you mentioned.

I need the proof that A does not depend on f, or if it does, how.

Anybody knows any more advanced physics forums?

20. Jul 10, 2009

### vin300

The extra variable is nothing but particle displacement.
The velocity is omega*sqrrt.(A^2-x^2)
After all that explanation tell me what tells you there is a link between A and f?
The average velocity is the average of the maximum velocity which is at the centre, A*omega and the minimum velocity 0 at the Amp.,A*omega/2 which is at x=sqrrt.(3)/2A and not x=1/2A as it is not uniform but oscillatory motion.
You got the relation between velocity and frequency
How do I get you a relation between A and f if it does not at all depend on f?

Last edited: Jul 10, 2009