Poroacoustic acceleration waves in a Jordan-Darcy-Cattaneo material

We present a theory for flow through a porous material in which the saturating fluid is such that the porosity is not too large. To achieve this we begin with the classical law of Darcy but argue that the pressure gradient will not have an instantaneous effect on the velocity. Rather, there will be a time delay. In this manner we produce a theory where the wavespeed of a non-linear wave travelling through the porous material depends explicitly on the parameters defining the fluid and the porous skeleton. We believe such a model and the resulting wave propagation analysis will be of interest to practitioners in the sound insulation industry. Exact expressions are provided for wavespeeds and wave amplitudes and these should be directly applicable to situations of immediate interest in soundproofing.