Interaction of Cylindrical Sound Waves with a Stationary Shock Wave

The interaction of cylindrical sound waves with a stationary shock is investigated by a method analogous to that used by H. Weyl in his treatment of the propagation of radio waves over the surface of a plane earth. The incident cylindrical sound wave is represented as a superposition of plane sound waves of varying direction. Each of the plane waves in this superposition interacts with the shock giving rise to a previously determined distortion of the shock front and reflected or refracted wave field; the cylindrical wave causes a disturbance which may be written in integral form as a superposition of these plane waves. The resulting interaction integrals are evaluated asymptotically to give explicit formulas for the distortion of the shock, the sound field, and the entropy-vorticity wave.