The spherical wave absorption coefficient of a patch of material

Recently, the concept of a spherical wave absorption coefficient, aspher, was introduced [M. A. Noblie, Proc. NOISE-CON 88, 567–572 (1988)] to account for the fact that when spherical waves are incident upon an acoustical material, the absorption coefficient is not the same as it would be under (less realistic) plane-wave incidence. In fact, aspher is not an intrinsic property of the material but depends on the distance of the sound source from the material. In this paper, an expression for the spherical wave absorption coefficient of a finite-size patch is derived (in the cylindrical coordinate system considered, the patch is either a circular or annular disk). As will be shown, this quantity can be approximated experimentally from measurements of the reflection coefficient at several oblique angles over the surface of the sample using the two-microphone transfer function method in a hemianechoic environment [an extension of M. A. Nobile, Proc. NOISE-CON 87, 611–616 (1987)]. This can be the basis for a simplified method of comparing the absorptive properties of two materials.