Speed of an air molecule when transmitting sound of frequency f

[luckis11]

According to their logic the average speed is 4Af and the the max speed is 2πAf.
The average speed is wrong, thus the max speed most probably wrong for the same reasons. Because when f tends to zero, the speed does not tend to zero.

Also, if we consider A to be the actual displacement of the molecule, then the factor A is correct. But we consider that when there is no sound, A is zero, thus the factor A is also wrong.

I guess these equations would be correct if the molecule was still when there is no sound.
The molecule is making a difinite number of oscillations (which is not definded by f) within a definite distance (which is not 2A) in each sec, when there is no sound.

Therefore, someone must find the correct equation. If I am wrong show me why.
My mistake could be that we can consider the speed of the molecule as zero when there is no sound, but why-how? Vin, don't say again that the average speed is zero "in all directions", because according to this logic, the speed in the above equations should also be zero.

 

[AIR&SPACE]

Therefore, someone must find the correct equation. If I am wrong show me why.
My mistake could be that we can consider the speed of the molecule as zero when there is no sound, but why-how? Vin, don't say again that the average speed is zero "in all directions", because according to this logic, the speed in the above equations should also be zero.

I was just walking back from the library restrooms and noticed a book called, "A Textbook of Sound" and immediately thought back to this thread. I have just picked out some passages that I looked quickly at. Take it for what it's worth.

"A Textbook of Sound" 3rd Rv. A.B Wood cpyrt 1955. G.Bell and Sons Ltd.

Pg 248 - 249 "velocity of small amplitude waves" excerpts

\sqrt{\overline{u^2}}=482 metres/sec
= root mean square velocity ;

\bar{u}=447metres/sec
= mean velocity of molecules

The Kinetic Theory of Gases shows very simply that the pressure in a gas is given by
P=\frac{1}{3}Nm\overline{u^2}=\frac{1}{3}\rho\overline{u^2}

where \\N is the number of molecules per c.c., \\m the mass of a molecule, and \rho the density of the gas.

This relation expresses the molecular velocity in terms of the pressure and density of the gas, thus
\overline{u^2}=\frac{3P}{\rho}

Since the energy of the motion of the molecules in a given (i.e. x-axis) we may write
speed of sound = \sqrt{\overline{u_{x}^2}}=\sqrt{\frac{P}{\rho}}

Which is Newton's "Isothermal Velocity" of wave-propagation in the gas. If we employ the mean molecular velocity \bar{u} instead of \sqrt{\overline{u^2}}
we find
\sqrt{\overline{u^2}}=\bar{u}\sqrt{\frac{3\pi}{8}}

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Pg 275-276 "Velocity of Sounds of High Frequency -- in Gases" excerpt

H.O. Kneser, in a number of theoretical and experimental papers dealing with anomalous absorption and dispersion of sound, has derived the following expression for the velocity in terms of frequency, \\w=2\pi\\N, and molecular constants:
\\v=\sqrt{\frac{P}{\rho}}\left(1+R\frac{c_{v}+w^2\beta^2c_{va}}{c_{v}^2+w^2\beta^2c_{va}^2}\right)
where \\c_{v} is the molecular heat at constant volume, \\c_{va} is the specific heat of the translation degrees of freedom, \\R is the universal gas constant, and \beta is the mean life of the energy-quantum, that is the time involved in the quantum transformation -- translational-intramolecular-translational energy.


at low frequencies the velocity becomes \sqrt{\frac{P}{\rho}}\left(1+\frac{R}{c_v}\right)

whereas at high frequencies it becomes \sqrt{\frac{P}{\rho}}\left(1+\frac{R}{c_va}\right)
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Anyways it appears to me that you should be able to substitute around and solve for molecular velocity