Sound Propagation in Flexible, Porous Media

Abstract

A theory is developed for the propagation of plane, longitudinal waves through a material which is both flexible and porous. An idealized model is constructed consisting of an array of parallel elastic rods uniformly spaced in air. Viscous and inertial coupling forces, as well as pressure squeezing accompanying sidewise expansion of the rods, are responsible for interaction between the air and solid of the model. Two dilatational waves are found in the unbounded medium. The propagation constants describing these waves are written in terms of 6 dimensionless parameters characteristic of the model. Boundary conditions are introduced and an expression is obtained for the acoustic impedance at the front surface of a rigidly backed model of finite thickness. It is shown that viscous coupling forces are of predominant importance in controlling the amount of acoustic energy converted into heat at the internal surfaces of the material. Viscous coupling also determines the amount of energy transferred from the airborne sound waves to the interior of the solid where dissipation may take place if internal losses are appreciable. Preliminary data relating theory to experiment are presented.