Propagation of Weak Disturbances in a Gas Subject to Relaxation Effects

A generalized wave equation is derived for sound disturbances in a gas when relaxation effects connected with, for example, molecular vibration or dissociation are important. Solutions involving discontinuous wave fronts are presented, and it is shown that, under certain assumptions, the complete wave equation reduces to a variant of the telegraph equation. Detailed solutions are presented for disturbance fields produced by a wavy wall in subsonic and supersonic flow and a simple wedge in supersonic flow. This study is viewed as a step in the development of a theory of small disturbances of a high-temperature gas, as is found behind the shock in hypersonic flight.