On the possibility of delaying shock formation in finite amplitude sound beams through alteration of the source signal.

Abstract

It was pointed out by Rudnick [J. Acoust. Soc. Am. 30, 564–567 (1958)] that if a plane wave is generated in the form of a backward sloping wave through appropriate phasing of the higher harmonics, then the amplitude of the fundamental frequency received at a given location would be enhanced. Burns [J. Acoust. Soc. Am. 45, 210–213 (1969)] further noted that such a wave would form a shock at a farther distance than that for monochromatic input at the level of the fundamental. Rogers [private communication (1987)] suggested that this effect would be especially beneficial for a sound beam. If the region for shock formation could be moved from the near field, where the signal is quasiplanar, to the far field, where it propagates in a spherical manner, then the result would be a substantial enhancement in the shock formation distance, because of the slower rate at which nonlinear effects accumulate in the far field. The present work uses the NPE code modified for sound beams to test this possibility. The input for the analysis is a baffled piston whose vibration consists of a fundamental at fixed amplitude plus a second harmonic at arbitrary amplitude and relative phase. Results for the fundamental and second harmonic at various locations indicate that the improvement is negligible because of the relative phase shift associated with transition from near-field to far-field behavior.