THEORY OF HIGH-FREQUENCY SOUND-PROPAGATION IN A SPATIALLY INHOMOGENEOUS-MEDIUM

This paper examines the propagation of sound in a spatially inhomogene ous medium. The high-frequency sound field due to a monopole source in a range-dependent environment has been derived. The method of Liouvil le-Green transformation is extended to three dimensions hence enabling simplification of the governing wave equation. This simplification al lows the total sound field to be expressed in terms of an inverse Four ier integral which can then be evaluated asymptotically by the method of stationary phase. The present method contrasts sharply with the cla ssical ray method which requires an initial assumption of the form of the asymptotic solution. Nevertheless, it is shown that the amplitude and the acoustical path length of the propagated sound determined by t he present method agree with that determined by the classical ray meth od. This is perhaps not surprising because both methods exploit the as ymptotic behavior of the solution. The present method has the further advantage that it enables the sound field in close proximity to causti cs to be calculated in a straightforward manner. (C) 1996 Acoustical S ociety of America.