Effective impedance of surfaces with porous roughness: Models and data

Abstract

A “boss” formulation by Twersky [J. Acoust. Soc. Am. 73, 85–94 (1983)] enables prediction of the plane wave reflection coefficient from a surface composed of rigid-porous roughness elements embedded in an acoustically hard plane where the roughness elements and their mean spacing are small compared with the incident wavelengths. Predictions for air-filled porous roughness elements on a hard ground plane are compared with effective impedance spectra obtained from laboratory measurements over random distributions of polystyrene hemi-spheres, polyurethane pyramids, and sand hemispheroids on glass plates. Overall the predictions agree well with these data. To enable prediction of the effective admittance of rough porous surfaces, Twersky’s original formulation is extended heuristically. The resulting theory is compared with a previous model [J. Acoust. Soc. Am. 108, 949–956 (2000)], which is a heuristic extension of Tolstoy’s theory [J. Acoust. Soc. Am. 72, 960–972 (1982)] to include nonspecular scattering. The theories are found to give different predictions for relatively large bosses. The modified Twersky theory gives relatively good predictions of the effective impedance spectra obtained from complex sound pressure level measurements over sand surfaces containing semielliptical roughness elements and over uncultivated soil.