Acoustic wave propagation in equivalent fluid macroscopically inhomogeneous materials

A one-dimensional problem of propagation of plane harmonic wave in macroscopically inhomogeneous materials is analyzed. A general description is proposed for the material of the equivalent fluid type characterized locally by two acoustical parameters: the wavenumber and the acoustical impedance. The coupled system of ordinary differential equations for amplitudes of forward and backward waves is derived. As an example the problem of wave interaction with a layer of inhomogeneous material placed between two homogeneous halfspaces is considered. The analytical solution and explicit expressions for reflection and transmission coefficients are obtained. It is shown that the presence of the inhomogeneous transition layer causes strong frequency dependence on both coefficients.