Sound Propagation in a Wedge with a Rigid Bottom

Sound propagation in a wedge with perfectly reflecting boundaries is one of the few range-dependent problems with an analytical solution. Since sound propagation towards the wedge apex will be completely backscattered due to the perfectly reflecting boundaries, this test problem is an ideal benchmark for a full two-way solution to the wave equation. An analytical solution for sound propagation in a wedge with a pressure-release sea surface and a pressure-release bottom was presented by Buckingham et al. [J. Acoust. Soc. Am. 87 (1990) 1511]. The ideal wedge problem with a rigid bottom is also of great importance in underwater acoustics. We present an analytical solution to the problem with a wedge bounded above by a pressure-release sea surface and below by a rigid bottom, which may be used to provide informative means of investigating the sound field in depth-varying channels, and to establish the accuracy of numerical propagation models for which it is difficult to treat problems with a pressure-release bottom. A comparison of the analytical solution and the numerical solution recently proposed by Luo et al. [Chin. Phys. Lett. 29 (2012) 014302] is also presented, indicating that this numerical propagation model provides high accuracy.