Oblique reflection of inhomogeneous acoustic waves

Abstract

An inhomogeneous plane wave, i.e., one having an exponential decay across the wavefront, may be used to model the sound incident on any reflecting boundary. If the decay is away from the boundary there is normally an element of reflection gain associated with the process, corresponding to a release of previously stored energy. This gain is in addition to the loss expected for an equivalent homogeneous wave. It is shown that the gain element is equal to the exponential decay in the inhomogeneous wave resolved across the horizontal beam displacement. This result holds very generally for transmission as well as reflection, for change of wave type, and for the gain element occurring when the incidence medium is lossy. In application to guided waves these results automatically ensure that the attenuation rate is the same, whether modeled by inhomogeneous waves with an element of gain, or by waves with a beam displacement. The incident inhomogeneous wave may be decomposed into a spectrum of homogeneous plane waves having a spread in angle. Similarly an attenuating mode may be regarded as propagating with a spread in equivalent ray angles.