Simple, relaxational models for the acoustical properties of porous media

By viewing thermal and viscous diffusion in porous media as relaxational processes, a particularly simple, phenomenological model for sound propagation in these materials is developed. The relaxation model parameters (characteristic times) are chosen by comparison to three existing models. Delany and Bazley's empirical equations; the Biot-Allard microstructural model; and Champoux and Stinson's generalized, microstructural model. It is shown that the relaxation model can effectively mimic the Delany-Bazley equations in their valid frequency range; yet, unlike the Delany-Bazley equations, the relaxation model has the advantage providing of realistic predictions at a broad range frequencies. In more exacting applications the characteristic times can be selected in a manner that makes the relaxation model predictions practically indistinguishable from the two microstructural models. The advantage of the relaxation model in these applications is its simple equations.