# How Does the Mean Free Path Affect Acoustic Wave Continuity?

• dara bayat
In summary, the conversation discusses the relationship between mean free path and pressure acoustics, specifically in regards to the minimum displacement of a wave in air. The mean free path in air is around 60nm, but a mosquito 3 meters away can create a displacement of 10nm which is above the hearing threshold for humans. The question posed is how the continuity assumptions of classical acoustics are preserved in this scenario. It is explained that while individual displacements will vary, the average displacement of 10nm is well-defined. The conversation concludes with a request for resources on calculating the theoretical limit of movement for creating an acoustic wave.
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.

Last edited:
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.

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

## What is the mean free path in acoustics?

The mean free path in acoustics is the average distance a sound wave travels before encountering an obstacle or boundary. It is a measure of the distance a sound wave travels through a medium before being scattered or absorbed.

## How is the mean free path related to sound propagation?

The mean free path directly affects sound propagation, as it determines how far a sound wave can travel before losing energy or being reflected. Longer mean free paths result in greater sound propagation, while shorter mean free paths lead to more attenuation and weaker sound propagation.

## What factors affect the mean free path in acoustics?

The mean free path in acoustics is affected by several factors, including the type and density of the medium through which the sound is traveling, the frequency and intensity of the sound wave, and any obstacles or boundaries in the medium.

## How is the mean free path calculated?

The mean free path can be calculated by dividing the average distance traveled by the number of collisions or interactions the sound wave has with particles in the medium. This calculation can be complicated and may require knowledge of the specific properties of the medium.

## Why is the mean free path important in acoustics?

The mean free path is an important concept in acoustics because it helps us understand how sound waves travel through different mediums and how they interact with obstacles and boundaries. It also plays a crucial role in determining the quality and clarity of sound in various settings and environments.

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