Simulating the effect of soft undulating surface on outdoor noise propagation using equivalent sources

Noise generated by large explosions at military bases causes discomfort to residents living in the vicinity, for up to 20km away. This noise explosion has strong low-frequency content and can travel over long distances. The attenuation of this acoustic wave depends on the shape of the surface. Calculating a faraway acoustic field above an undulating soft surface is difficult. The complex equivalent source method (CESM) is employed here to model the acoustic transmission loss over the undulating soft surface for a low-frequency harmonic excitation. The softness is represented by additional sources which are paraxial to the image source with complex locations. This integral is known to be convergent for acceptable impedances. Additional sources are used to account for the undulation, and their amplitudes, phases and locations are determined by solving a least-square problem derived from the boundary conditions. The method then estimates the pressure field using superposition of the effect of the equivalent sources. We simulated the method for single harmonic excitations and for different surface geometries and impedances.