Differential Geometry and Acoustics: A Survey

Abstract

A connection between acoustic rays in a moving inhomogeneous fluid medium and the null geodesic of a pseudo-Riemannian manifold provides a mechanism to derive several well-known results commonly used in acoustic ray theory. Among these include ray integrals for depth dependent sound speed and current profiles commonly used in ocean and aero acoustic modelling. In this new paradigm these are derived by application of a symmetry of the effective metric tensor known as isometry. In addition to deriving well-known results, the application of the full machinery of differential geometry offers a unified approach to modelling acoustic fields in three dimensional random environments with time dependence by, (1) using conformal symmetry to simplify the geodesic equation, and (2) application of geodesic deviation as a generalization of geometric spread.