Spreading Loss of Sound in an Inhomogeneous Medium

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Abstract
Geometric spreading of sound in a medium with any given continuous velocity profile is investigated theoretically. The sound velocity is assumed to be dependent on one space coordinate only. The analysis is based on Snell's law. Time and initial angle of the ray are the two independent variables. A set of differential equations describing spreading loss is developed. These equations are solved analytically for the case of constant‐velocity gradient yielding well‐known results. A short discussion of both analog‐ and digital‐computer solutions for the general case is given. Discontinuous velocity profiles and the interchange of sound source and receiver are also considered.

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