Estimation of acoustical materials sound absorption coefficient under oblique incidence plane wave and diffuse field via Allard model inversion

A technique for estimating the sound absorption of materials under oblique incidence plane wave and diffuse field excitations is proposed. It requires a mobile loudspeaker and a pair of fixed microphones above a layer of absorbing material. Starting from sound pressure measurements made above the material surface for multiple source positions and by inverting Allard's propagation model, the proposed method allows for the identification of two effective (or equivalent) parameters, namely, the complex effective density and the complex wave number. Obtaining these parameters makes it possible to estimate the sound absorption coefficient for a plane wave with any angle of incidence or under a diffuse acoustic field by summation over the angles. The results are compared to theoretical values calculated using the Johnson-Champoux-Allard model and to reference measurements obtained using an impedance tube, a small cabin, a large reverberant room, and a sound field synthesis method. One of the limitations of this method lies in the assumptions associated with the Allard model to describe the sound field above the material (assumed to be isotropic, homogeneous, of constant thickness, and to behave like an equivalent fluid). The main advantages are (1) that the sound absorption coefficient can be estimated under oblique incidence plane wave and diffuse acoustic field with values that are always in a physical range (between 0 and 1), and (2) that samples of the order of the square meter without specific preparation can be tested which reduces the constraints associated with impedance tube or reverberant room measurements.