Sound Absorption and Velocity in Mixtures

The effects of (a) collision excitation probabilities dependent on the internal energy specification of the impinging molecules; (b) transitions in both colliding members; (c) triple and higher order collisions; (d) viscosity and conduction, are considered with reference to sound propagation. A comparative study is made of the generalized Kneser-Ruttgers method and the writer's method of investigation. It is shown that the two are developments of the same physical theory and may be looked upon as a thermodynamic and a kinetic theory transcript respectively. In particular, ${\omega }_i$ (a parameter, dependent on the frequency, which determines the degree to which equilibrium conditions are attained) plays a central role, implicitly, in the former method as well as in the latter. The kinetic theory transport equation interpretation of the use of $C_{\infty }$ instead of $\frac{3k}{2}$ is noted. It is shown that for impurity contamination, the Kneser special assumptions and formulae fall out as consequences of the general mixture theory if certain approximations are valid. The triple collision hypothesis for H, O, ${\mathrm{O}}_2$ mixtures is discussed and alternative explanations are suggested. The main contributions of this paper from the experimenter's view-point are the formulae for absorption and velocity in mixtures, derived by the two methods referred to above, in convenient form for application.