Sound propagation through a rarefied gas confined between source and receptor at arbitrary Knudsen number and sound frequency

Abstract

A sound propagation through a rarefied gas is investigated on the basis of the linearized kinetic equation taking into account the influence of receptor. A plate oscillating in the normal direction to its own plane is considered as a sound source, while a stationary parallel plate is considered as being the receptor of sound. The main parameters determining the solution of the problem are the oscillation speed parameter, which is defined as the ratio of intermolecular collision frequency to the sound frequency, and the rarefaction parameter defined as the ratio of the distance between source and receptor to the molecular mean free path. The kinetic equation is solved via a discrete velocity method with a numerical error of 0.1%. The numerical calculations are carried out for wide ranges of the oscillation and rarefaction parameters. The concept of integral phase parameter is introduced to obtain the sound speed correctly in all regimes of the gas rarefaction and sound frequency. Analytical solutions are obtained in the limits of small and large parameters of frequency and rarefaction.