Free-Molecule Expansion Polynomials and Sound Propagation in Rarefied Gases

In the asymptotic evaluation of certain integrals in the method of Kahn and Mintzer describing high‐frequency sound propagation, certain errors occur. These have been described and corrected in an attempt to obtain a valid description of sound dispersion and attenuation over a wide range of frequencies. However, the corrected asymptotic results fail to yield physically acceptable modes of propagation for all values of the rarefaction parameter $\mathrm{\tau \hspace{0.17em}=\hspace{0.17em}p/\omega \mu }$ . Only for small values of the rarefraction parameter (the high‐frequency limit) are suitable descriptions of experimental results obtainable. The physical and mathematical reasons for the failure of free molecule expansion polynomials to predict continuum sound modes are discussed.