A Comparison of Three Methods to Calculate the Surface Impedance and Absorption Coefficient from Measurements Under Free Field or in situ Conditions

In this paper the measurement, in situ or under free-field conditions, of the surface impedance and absorption coefficient is investigated. Numerical simulations of the measurement of impedance above a locally reactive surface is performed with the Boundary Element Method (BEM). Experiments are also made in a semi-anechoic chamber and in a regular office room. Three calculation methods used to obtain the surface impedance of an absorbent surface are described and compared, two of them being iterative. The first, referred to herein as the "q-term", relies on an exact description of the sound field above an infinite locally-reactive plane. The second, the "F-term", relies on an approximation for large values of the argument k |r ₂ ^→| in its equations. The third, the "Plane Wave Approximation (PWA)", is a simplification of the spherical wave reflection which considers that the reflected wave has its amplitude and phase changed by a simple planar reflection coefficient. The "F-term" and the "Plane Wave Approximation" methods also assume an infinite locally-reactive plane. The three calculation methods are compared, the differences in the found results are discussed. The three methods are compared mainly for small sound-source to sensor distances (|r ₂ ^→| = 0.3 m) and it is seen that they tend to converge as this distance increase. This comparison is relevant to in situ impedance measurements, since a bad choice of the calculation method may lead to a poor result.