Kinetic Theory of Sound Propagation in Rarefied Gases

The problem of sound propagation in highly rarefied monatomic gases is investigated from the point of view of general orthogonal polynomial solutions (in velocity space) of the Boltzmann equation. It is shown that the usual expansion solutions of the Boltzmann equation (Chapman-Enskog-Burnett, and Grad) are not valid for this problem. Solutions, instead, are obtained by means of an expansion of the distribution function in a set of velocity polynomials which have been orthogonalized with respect to a zero-order distribution function characteristic of a collisionless gas, rather than a Maxwell distribution function as is usually done. These solutions are used to derive absorption and dispersion functions characterizing the sound propagation. These are shown to be in agreement with experimental data for the problem.