Abstract
It follows from an examination of the dispersion relation in the free-molecule flow limit that the superposition of the different modes can lead to a solution of the boundary value problem of sound propagation in the low density limit. Therefore, a procedure, based on the moment method for solving the full Boltzmann equation, is developed to superimpose the modes found to be present from the dispersion relation. This procedure can be used to determine the boundary value sound distribution function to any order of approximation. Applying this technique to the 13-moment equations, the boundary value problem of sound propagation in a monatomic gas is solved by superimposing the two modes associated with this approximation.
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