Propagation of Forced Sound Waves in Rarefied Gasdynamics

* Present address: Applied Mathematics Department, Brookhaven National Laboratory, Upton, New York. • See, for instance, L. Landau and E. Lifshitz, Fluid Mechanics (Addison-Wesley Publishing Co., Inc., Reading, Mass., 1959). scribed by the classical theory of Stokes and Kirchoff. • This theory is, of course, based on the Navier-Stokes equations. However, for high-frequency sound propagation in a low-pressure gas, we can expect he situation to change markedly. The relevant parameter is the Knudsen umber (Kn), i.e., the ratio of gas mean free path to sound wavelength (alternately, the ratio of sound frequency to gas collision frequency). To obtain a theory for larger values of Kn one has no recourse but to turn to the Boltzmann equation of kinetic theory. Attempts at the sound problem, based on kinetic theory, have been made by Wang Chang •' (Burnett equations) and by Wang Chang and Uhlenbeck a (super-Burnett equations). However, comparison of these theories with experiment 4.5 shows that these are at best slight extensions of the Navier-Stokes results. Pekeris and his coworkers 6.7 using numerical procedures have extended