On the use of the local reflection coefficient to assess the diffuse field sound absorption coefficient of a porous material

The diffuse field sound absorption coefficient (SAC) of a sound absorber can be obtained from an average over the incidence angles of the oblique incidence plane wave SAC. The plane wave SAC can be derived from the plane wave complex-valued reflection coefficient defined as the ratio of the reflected sound pressure at a given point on the material surface to the incident sound pressure at the same point. In practice, the material is excited by a monopole, and the reflection coefficient becomes a local quantity which is a function of the source height and the radial distance from the source. This local reflection coefficient obtained at various points on the material surface is commonly used to approximate the oblique incidence plane wave reflection coefficient. The error in estimating the diffuse field SAC introduced by this approximation has not been explored in the literature. This paper investigates this error as a function of the material extent, thickness, and source height using an analytical approach to calculate the local reflection coefficient. The calculation is based on Allard’s model which describes the sound propagation above an infinite lateral extent porous material backed by a rigid wall and excited by a monopole. Using finite element simulations as a reference, the analytical model is shown to provide a good approximation of the diffuse field sound absorption performance of sufficiently large material areas. The diffuse field SAC calculated from plane wave reflection coefficients and local reflection coefficient are compared. The limitations inherent in deriving diffuse field SACs from local reflection measurements obtained with a monopole are highlighted.