The acoustical equivalence principle for ray tracing

Abstract

While the acoustical wave functions for various acoustical problems can be mapped into each other by a coordinate transformation (the acoustical equivalence principle), the corresponding ray tracings cannot be so mapped. Applying the acoustical equivalence principle [A. E. Faraggi and M. Matone, Int. J. Mod. Phys. A 15, 1869–2017 (2000) for the analogous quantum equivalence principle] to the underlying acoustical Hamilton–Jacobi equation for ray tracing renders a modified acoustical Hamilton–Jacobi equation which does obey the quantum equivalence principle. Solutions of the modified acoustical Hamilton-Jacobi equation, which are either acoustical Hamilton’s principal function or the acoustical reduced action (acoustical Hamilton’s characteristic function), are the generators of motion for rigorous ray tracing.