Page:Threeshockwaves.pdf/1



1. . J. von Neumann has studied the problem of the reflection of shock waves by a rigid plane surface and finds that for a given intensity of the incident shock (as specified for instance by the ratio of the pressures $$\zeta$$ on the two sides of the shock front) regular refection can take place only for angles of incidence $$\alpha$$ less than a certain critical value $$\alpha_{\mathrm{extreme}}(\zeta)$$.



Moreover, for a value $$\alpha<\alpha_{\mathrm{extreme}}(\zeta)$$ two solutions are possible. It is, however, generally supposed that the solution with the smaller of the two possible values $$\alpha'$$ represents physically realizable solution. The reason for this supposition is that in the acoustic limit $$\zeta=1$$ the solution with the smaller $$\alpha'$$ passes continuously into what is believed to be true for the sound waves (namely $$\alpha=\alpha'$$).

The question arises as to what happens when $$\alpha>\alpha_{\mathrm{extreme}}(\zeta)$$. Von Neumann suggests that for angles of incidence of a shock wave greater than the critical value the Mach effect takes place (Fig. 2),