Velocity and absorption coefficient of sound waves in classical gases

TL;DR

This paper derives and solves a dispersion equation for sound waves in classical gases, revealing universal behavior of sound velocity and absorption coefficient across collision regimes, consistent with experimental data.

Contribution

It introduces a nonperturbative dispersion equation within linear response theory and numerically solves it to analyze sound wave behavior in gases.

Findings

Sound velocity increases sharply near $ ext{ωτ} ext{~1}$ transition

Scaled absorption coefficient reaches a maximum at this transition

Results agree with experimental observations

Abstract

Velocity and absorption coefficient of the plane sound waves in classical gases are obtained by solving the Boltzmann kinetic equation. This is done within the linear response theory as a reaction of the single-particle distribution function to a periodic external field. The nonperturbative dispersion equation is derived in the relaxation time approximation and solved numerically. The obtained theoretical results demonstrate an universal dependence of the sound velocity and scaled absorption coefficient on variable $\omega\tau$, where $\omega$ is the sound frequency and $\tau^{-1}$ is the particle collision frequency. In the region of $\omega\tau\sim 1$ a transition the frequent- to rare-collision regimes takes place. The sound velocity increases sharply, and the scaled absorption coefficient has a maximum -- both theoretical findings are in agreement with the data.