On the theory of sound transfer in rigid-frame porous materials

The modeling of the macroscopic propagation of sound inside porous media is usually based on first order acoustical quantities. Single or multiple layers are treated as an equivalent impedance network which can be also solved with a transfer matrix formulation. In this work the one dimensional, time averaged, macroscopic sound transfer process in rigid-frame porous media is reinterpreted with the concepts developed in the field of sound intensity. An algebraic derivation shows that the active intensity is proportional to the spatial gradient of the sound energy density, so that the two quantities obey a diffusion equation. The name sound conductivity is suggested for the related coefficient, and the expressions of the sinks of sound energy and of the sources of reactivity in the material are formalized. Moreover a differential formulation for the energy densities inside the material is developed and solved analytically.