The Dispersion Relation Of Sound Propagation In Gas-Mixture

The dispersion relation(namely the relation between the frequency and the wave number of the sound wave at the media) is of importance in studying of the sound propagation problems. Many of the studies of the dispersion relation are contacted with the macro Navier-Stokes methods. In paper [l],the author investigated the dispersion relation in simple gas with kinetic theory. In this paper, we try to the dispersion relation of sound propagation in gas-mixture with kinetic theory. At first, we give the eigenvalues and eigenfunctions of the linearized Boltzmann equations in gas-mixture ,then establish the model equations of the linearized Boltzmann equations,at last we give the equation by the Fourier-Laplace transform and the dispersion relation. Here we also give some analysis of it.