Sonic boom beyond the carpet edge

Abstract

Geometrical acoustics predicts the amplitude of some booms only within the carpet. Inside the geometrical shadow zone, a new, nonlinear, time-domain formulation of diffraction effects is given. A comparison of magnitude orders shows that nonlinear effects are expected to be small, except in the case of small sound speed gradients. In the linear case, the usual dispersion equation for creeping waves is recovered. The matching to geometrical acoustics yields an analytical expression for the pressure in the shadow zone, under the form of a series of creeping waves. Numerical simulations show that the amplitude decay of the signal compares favorably with Concorde sonic boom measurements, while the magnitude order of the rise time is correct. The ground impedance is shown to influence mostly the rise time and amplitude of the signal close to the carpet edge.