The propagation of ultrasound of frequency ω through a classical, dilute, monatomic gas is studied in terms of the Boltzmann collision equation. The collision term is replaced by the relaxation model
, where f̄
is the displaced Maxwellian distribution in the presence of the sound wave and the relaxation time τ does not depend on the instantaneous particle velocity. Once the form of f
is determined, the homogeneous equations corresponding to number, momentum, and energy conservation are written down. Setting the determinant of the coefficients of the unknowns in these three equations equal to zero yields the general dispersion relation, relating the complex wavenumber k = k1+ik2 ≡ (ω/V)+iα
to ωτ. Two special cases are studied: namely, ωτ < < 1 and ωτ > > 1. For the former, our results agree qualitatively with those of Wang‐Chang and Uhlenbeck and with experiment. For ωτ > > 1, it is found that the amplitude absorption coefficient α increases linearly with ω while the phase velocity V
becomes independent of frequency. Furthermore, a spectrum of such absorption and dispersion curves is found for which there is, at present, no satisfactory physical explanation. At this time, there are no valid experimental data in existence to confirm or disprove our high‐frequency results.