Analysis of the sound field above finite absorbers in the wave-number domain.

This study examines the edge diffraction effect when a sound wave impinges and reflects off finite porous absorbers, flush-mounted in an infinite hard baffle. A theoretical analysis of the diffraction is given by taking a two-dimensional spatial Fourier transform of a plane wave impinging on a finite absorber. Numerical experiments are also presented to simulate the sound field above infinite and finite locally reactive absorbers and the measurement with an array of pressure sensors. In such cases, a regularized solution is used to separate the incident and reflected plane wave components, in the wave-number domain, including both propagating and evanescent waves. The properties of the wave-number spectrum are associated either with the specular reflection or with the diffracted components, caused by the interaction of the sound wave with the finite absorber. From the regularized solution, it is possible to reconstruct the surface impedance and the absorption coefficient of the sample. The influence of Gaussian noise on such measurements is also investigated. The use of propagating and evanescent waves on the sound field model led to an estimation of the absorption coefficient that depends just slightly on the size of the sample, which is a desired feature for in situ measurement methods.