Ground effects: New analytical approximations and experimental results

Abstract

Analytical approximations for the sound field produced by a point source S in the presence of a ground have recently been developed [D. Habault, J. Sound. Vib. 68(3) (1980)]. The sound pressure at a point x can be expressed by a convergent series: p(x) = −exp(ikr)4πr + ∑ n=0∞ Λn⋅A(θ) exp(ikR)4πR + exp(ikR)4πR ∑ n=0∞ FnRn (R,θ), where r = SX, R the distance to X from the image source, A(θ) the plane wave reflection coefficient, and Λn a differential operator with respect to θ of order 2n. An approximation of the farfield is obtained by taking into account only the first terms of the series: the terms of the second series, called complementary terms, provide a better description of the field when R is not so large and can be neglected when R is very large because the functions Fn(R,θ) decrease exponentially with R. Measurements made in France and Canada over grassy ground show fair agreement between theory and experiment in the asymptotic region when the ground is characterized by a complex specific normal impedance. At low frequencies (∼500 Hz) prediction is not as good due to the fact that a better model for ground should be used, for instance, a finite or infinite thickness layer of porous medium.