The decay of the shock wave from a supersonic projectile

In the case of a sound wave from a supersonic projectile of any shape, it has been found that the wave profile, at a certain distance from the source, involves a front shock and a tail shock. The asymptotic decay of these two shocks of equal magnitude has been studied by Lighthill (1978), Pierce (1981), and Whitham (1974). However, the inviscid wave theory used in these studies cannot account for the vanishing of the shock. The present study uses an approach involving the employment of a generalized Burgers equation for cyindrical waves, taking into account an investigation conducted by Enflo (1981). The result of this investigation is used to give the amplitude and the smooth profile of the sound pulse from a supersonic projectile at distances so far from the source that the shock has broadened and disappeared.