Simulation Of Sound Propagating Over Soft Surface Using The Equivalent Source Method

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. Most of the theoretical and experimental work that has been done to study and reduce this type of noise involved the use of barriers and sound proofing the residential houses. In this thesis, we consider the application of reducing the acoustic noise by shaping the landscape. The solution of this problem is difficult due to the semi-infinite domain, especially in the case of soft ground. To overcome the difficulty of calculating a faraway acoustic field for an undulating soft surface, we use the Equivalent Source Method (ESM) as a generalization of the image source method which is applicable to flat surfaces only. Additional sources are used to account for the undulation, and their amplitudes and 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. In short, the acoustic field caused by a source above an impedance plane is computed by using a superposition of equivalent point sources located below the surface. A special notation is derived to simplify this formulation. To account for finite impedance, we incorporate an integral introduced by Ochmann [31] which represents additional sources located at complex locations paraxial to the image source. This integral is known to be convergent for acceptable impedance. The boundary conditions are then updated as to reflect the influence of the Ochamann term, and the matrices involved in the least-squares solution now have six additional terms. The proposed method is then applied to a sinusoidally varying surface. To simplify the calculation, the positions of the equivalent sources are postulated to be a small distance below the2 surface to avoid unnecessary complications due to singularity within the domain. Subsequently the complex amplitudes are derived by enforcing the boundary conditions at a number of test points chosen along the flat and the undulating parts of the surface. The resulting equivalent sources presented inversely decaying amplitudes as expected and their phases presented an expected pattern. Subsequently, we computed the pressure at the far field and both the undulation and the impedance were shown to contribute to the suppression of the acoustic field faraway