Geometrical Acoustics. I. The Theory of Weak Shock Waves

Abstract

In the first part the discontinuity conditions in an arbitrary continuous material are deduced for a general (i.e., possibly curved) discontinuity surface. It is then shown that only three types of discontinuities are possible—shocks, contact discontinuities, and phase‐change fronts. In the second part the acoustic discontinuity conditions are deduced and specialized to a perfect fluid without heat conduction. Then a first‐order partial differential equation is obtained for the location of an acoustic shock front. This equation can be solved, as in optics, by means of rays. The variation of shock strength along a ray is then determined (this is one main result of this paper). Coefficients of reflection and transmission for an acoustic shock at a contact discontinuity in the basic flow are also obtained. Finally, the results are exemplified by an analysis of the shock tube.