How Does the Mean Free Path Affect Acoustic Wave Continuity?

[dara bayat]

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

 

[mfb]

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.

 

[dara bayat]

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