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.

Using natural means to reduce surface transport noise during propagation outdoors

“…there is significant coherent scattering and reflection) there can be a significant change in ground effect. Many laboratory experiments have shown that the influence of small scale roughness on propagation over hard and soft surfaces can be considered in terms of effective surface impedance [38][39][40]91,92]. Particularly if the surface is acoustically-hard, roughness induces a surface wave.…”

“…Several papers have reported laboratory data showing that the effect of adding small scale roughness to a surface, whatever its original impedance, is to modify its impedance [3,85,91,92,98]. If the original smooth surface is acoustically-hard then the effective impedance of the roughened surface is finite.…”

Exploiting ground effects for surface transport noise abatement

“…There is considerable laboratory data showing that the effect of adding small scale roughness to a surface, whatever its original impedance, is to modify its apparent impedance [2,[28][29][30][31][32]. If the original smooth surface is acoustically-hard then the effective impedance of the roughened surface is finite.…”

“…there is significant coherent scattering and specular reflection) there can be a significant change in ground effect. Many laboratory experiments show that the influence of small scale roughness on propagation over hard and soft surfaces can be considered in terms of effective surface impedance [2,[28][29][30][31][32]. Also, particularly if the surface is acoustically-hard, roughness induces a surface wave.…”

A Wavenumber Independent Boundary Element Method for an Acoustic Scattering Problem

“…This problem has attracted much attention in the literature (see, for example, [17,30,31,16,21,6,48]), both in its own right and also as a model of the scattering of an incident acoustic or electromagnetic wave by an infinite rough surface [8,47,36,7]. In the case in which there is no variation in the acoustical properties of the surface or the incident field in some fixed direction parallel to the surface, the problem is effectively twodimensional.…”