New empirical equations for sound propagation in rigid frame fibrous materials

TLDR

Sound propagation in fibrous materials depends on fiber diameter and material density, as suggested by the model used. The authors derived the expressions using Johnson et al.'s general frequency dependence of viscous forces in porous materials and transposed the model to predict the dynamic bulk modulus of air. The new expressions match Delany–Bazley predictions within its range and remain accurate at low frequencies where Delany–Bazley gives unphysical results. J.

Abstract

New expressions are given that can be used instead of the phenomenological equations of Delany and Bazley. They provide similar predictions in the range of validity of these equations, and in addition are valid at low frequencies where the equations of Delany and Bazley provide unphysical predictions. These new expressions have been worked out by using the general frequency dependence of the viscous forces in porous materials proposed by Johnson et al. [J. Fluid Mech. 176, 379 (1987)], with a transposition carried out to predict the dynamic bulk modulus of air. The model used suggests how sound propagation in fibrous materials can depend both on the diameter of the fibers and on the density of the material.