The scattering of sound by a long cylinder above an impedance boundary

Abstract

The classical problem of sound scattering by an acoustically hard cylinder due to a point monopole and a line airborne source is extended in the present study. The solution to the homogeneous Helmholtz equation is expressed in a cylindrical coordinate system and represented by an expansion of Fourier integrals. Incorporating the image source method and the Bessel function addition theorem, the analytical solution is derived for the prediction of multiple scattering of sound by a hard cylinder placed above a ground surface of finite impedance. The total sound field can be expressed as a sum of four components: the incident field, the reflected wave, and the scattered fields from the cylinder and its image. The total far-field scattered potential was evaluated asymptotically by the method of stationary phase. Experimental measurements by using a point source were conducted in an anechoic chamber to validate the theoretical formulations. The numerical predictions of using a point source model give good agreements with all the experimental data but there are obvious discrepancies in the spectral magnitudes between the calculation and experimental results when a line source model is used to simulate the scattering problem due to a point source excitation.