Acoustic fields in inhomogeneous media: Some exact harmonic solutions for variable area ducts and curvilinear geometries

The objective of this paper is to present exact harmonic solutions describing sound propagation through variable area ducts, having non-uniform mean temperatures. Using appropriate transformations, the wave equation is reduced to the Bessel's differential equation. Expressions are obtained for the acoustic pressure and velocity for a family of area and temperature profiles. Example calculations showing the application of these solutions are presented. The paper closes with the derivations of expressions for sound propagation in cylindrical and spherical co-ordinate systems.