Underwater Sound Pressure from Sonic Booms

An expression is derived for the sound pressure in a homogeneous fluid half-space, the surface of which is loaded by an idealized sonic-boom pressure signature. The expression is cast into dimensionless form and plotted as a function of time at three selected depths. In contrast to the abrupt beginning and end of the sonic-boom pressure variation in air, the pressure wave underwater is found to exhibit a precursor and tail. The underwater waveform is seen to be an odd function of time relative to the instant when the center of the sonic boom passes directly over the point of observation.