Sound absorption estimation using the discrete complex image source method and array processing

Abstract

Estimating the sound absorption of a material under realistic sound-field incidence conditions relies on accurately describing the measured data. Evidence suggests that modeling the reflection of impinging spherical waves is important, especially for compact measurement systems. This article proposes a method for estimating the sound absorption coefficient of a material sample by mapping the sound pressure, measured by a microphone array, to a distribution of monopoles, including the sound source and a series of complex image-sources. The proposed method is compared to modeling the sound field as a superposition of two sources (a monopole and an image source). The sound absorption measurement is tested with simulations of the sound field above infinite and non-locally reacting porous absorbers. The inverse problem estimations are compared to the classical plane-wave absorption coefficient and the one obtained by measuring the surface impedance when a spherical wave impinges on the absorber. Experimental analysis of two porous samples and one resonant absorber is also carried out in a laboratory. Two microphone arrays were tested with different apertures and number of sensors, and it was demonstrated that measurements are feasible even with the more compact array and for frequencies above 250 [Hz]. The discretization of the integral equation led to a more accurate reconstruction of the sound pressure and particle velocity at the sample’s surface. The resulting absorption coefficient agrees with the one obtained for spherical wave incidence, indicating that including the source and several complex image-sources is an essential feature of the sound field.