Sound penetration into a hard-backed rigid porous layer: Theory and experiments

Abstract

This study examines the sound field within a hard-backed rigid porous medium due to an airborne source. The total sound field can be approximated by two terms: A transmitted wave component arriving at the receiver directly through the porous interface, and a second transmitted wave component reflected from the rigid backing plane before reaching the receiver. These two components can be expressed in an integral form that is amenable to further analyses. A standard saddle path method is applied to evaluate the integral analytically, leading to a uniform asymptotic solution that allows the prediction of the sound field within the rigid porous medium. The validity of the asymptotic formula is verified by comparison with the numerical results computed by a more accurate wave-based numerical scheme. The asymptotic solution is shown to provide a convenient means of rapid and accurate computations of sound field within the rigid porous medium. The accuracy of the numerical solutions is further confirmed by comparison with indoor experimental results. The measurement data and theoretical predictions suggest that when the receiver is located near the bottom of the hard-backed layer, the reflection of the refracted wave gives rise to a significant contribution to the total sound field.