The reflected and transmitted acoustic field excited by a supersonic source in a two media configuration

摘要

The acoustic wave field due to a supersonic motion of a rigid object over a half-space is investigated. The analysis presented leads to closed form expressions for the reflected and transmitted conical waves as separate contributions. The linearized acoustic field equations are applied to obtain representations for the fields in a combined Laplace-Fourier transform domain. To these representations, which are mapped into the proper form, we apply the Cagniard-de Hoop technique in order to find closed form time-domain solutions for the reflected and transmitted acoustic fields. Attention is focused on supersonic effects, so the analysis concentrates on application of the Cagniard-de Hoop technique to obtain closed form space-time domain expressions from the contributions of poles, appearing in the transform domain representation for the reflected and transmitted acoustic wave field. It turns out that these pole contributions, next to wave solutions of the conical type also can give rise to headwaves, associated with the reflected conical wave. Numerical results for the reflected as well as the transmitted conical wave field are presented for an air-sea configuration with supersonic source velocities up to MACH 5.