Propagation of Sound in a Gas of Rigid Spheres

Abstract

The linearized Boltzmann integral equation for the problem of propagation of sound in a rigidsphere gas was solved by first determining the eigenfunctions of the collision operator and then solving the propagation matrix. Determinants up to order n = 105 were solved, and the results are illustrated. With the maximum order 105 of the matrix solved, the values of the propagation parameters obtained show convergence to within 2% for R > 1.8, where R = 2fc/3πf. The theoretical results are in fairly good agreement with Greenspan's measurements of the speed and attenuation of sound in rarefied helium.