Approximate impedance models for point-to-point sound propagation over acoustically-hard ground containing rectangular grooves. The Journal of the Acoustical Society of America, 147(1) pp. 74-84. For guidance on citations see FAQs.

Summary Regularly spaced low walls and rectangular lattices on a hard ground have been investigated as a means for reducing noise levels from surface transport. Predictions of the insertion loss of such surfaces has involved the use of computationally intensive numerical methods such as the Boundary Element Method (BEM) or Finite difference techniques (FDTD and PSTD). By considering point-to-point propagation above regularly spaced acoustically hard grooves with rectangular cross sections, a modal model used hitherto to predict electromagnetic and ultrasonic surface waves is adapted to derive an effective impedance for such a grooved surface. When this effective impedance is used in the classical theory for propagation from a point source above an impedance plane, the modal model enables predictions of excess attenuation spectra that compare closely with those obtained by numerical methods but take a fraction of the time. Also the modal method is extended to predict excess attenuation spectra above phase gradient metasurfaces with porous material in each constituent groove.

A modal model formulation explains many aspects of sound propagation over complex grooved surfaces. Insights that such a formulation offers about the intrinsic resonant properties of rectangular grooved surfaces shall be explored and applied to predict phenomenon such as surface waves and non-specular energy redistribution (blazing). Furthermore, the effects of filling the grooves with a porous material are investigated. A brief summary is made of the modal method and the mechanisms involved with sound propagation over rough surfaces to provide the context before exploring, in detail, how the modal method may be applied to predict various resonant behaviours of rectangularly grooved gratings. As well as their general predictive capabilities, the modal methods also provide significant insight into the wave modes diffracted by grooved surfaces under incident excitation at a low computational cost.

No abstract

Previous studies of airborne surface waves have been carried out at audio-frequencies over periodically rough surfaces formed by lighting lattices and bricks and at ultrasonic frequencies over mm scale compound gratings involving grooves of the same depth but different widths. In this paper, a modal model, which has been found to give comparable predictions to BEM while being much faster to run is used, together with BEM, to investigate audio-frequency sound propagation over grooves of varying widths and depths in the order of cm. Predictions of excess attenuation spectra, pressure contours and zeroes in the effective reflection coefficient over grooves with multiple widths and depths are used to indicate the nature of the surface waves which involve overlapping quarter wavelength resonances. Predictions are extended to multiple depth grooved surfaces without and with porous infills.