An Exact Wave Equation for Sound in Inhomogeneous, Moving, and Non-Stationary Fluids

Acoustic wave equation is typically the starting point in mathematical modeling of sound propagation, scattering, and diffraction as well as in solving inverse problems attendant to acoustic remote sensing. While acoustic wave equations are well known for motionless media, no exact, scalar wave equation has been found for sound in generic inhomogeneous, moving fluids. In this paper, an exact wave equation is derived which describes sound propagation and scattering in a wide class of inhomogeneous, moving fluids with time-dependent parameters. A number of previously proposed acoustic wave equations prove to be particular cases of the new equation.