How Does the Mean Free Path Affect Acoustic Wave Continuity?

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SUMMARY

The discussion centers on the relationship between mean free path and pressure acoustics, specifically how classical acoustic continuity is maintained despite the small displacements of air molecules. The formula for calculating wave displacement in air is presented as dp = v * rho * 2 * pi * freq * dx, with a noted minimum displacement of 10nm, which exceeds the 20uPa hearing threshold for humans. The mean free path in air is approximately 60nm, leading to questions about the continuity of molecular interactions in acoustic wave propagation. The conversation highlights the importance of averaging displacements over a large number of atoms to define mean displacements accurately.

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  • Understanding of pressure acoustics and wave propagation
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  • Knowledge of basic acoustic formulas and parameters
  • Experience with molecular dynamics and statistical mechanics
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dara bayat
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Hello everyone,

I have a question regarding the implication of mean free path and pressure acoustics.

I have seen several publications on the internet and also calculated the minimum displacement of a wave in air using the formula

dp=v * rho * *2*pi*freq. * dx

The values of displacement can be as low as Angstrom or even lower.

A mosquito 3 meters away could create a 10nm displacement of air which is above the 20uPa hearing threshold for humans. doi: 10.1098/rspb.2000.1021

The mean free path in air is around 60nm.

The question is how come the continuity assumptions of classical acoustics are preserved here?
In other words, I don't understand how we could talk about a wave if we don't have a continuity in the influence of the air molecules on each other.

Thanks in advance for your helpBest regardsDara
 
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It is an average displacement. The individual displacements will vary by at least these 60 nm, but averaged over something like 1020 atoms a mean displacement of 10 nm is well-defined.
 
mfb said:
It is an average displacement. The individual displacements will vary by at least these 60 nm, but averaged over something like 1020 atoms a mean displacement of 10 nm is well-defined.

thank you very much for your answer,

do you know of any book/article where the theoretical limit of movement for creating an acoustic wave is calculated/shown (considering the pressure/temperature as you have mentioned)?

thank you again for your help
Dara
 

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