Modeling the effects of hard undulating surfaces on outdoor noise using equivalent sources

The attentuation of acoustic waves propagating above hard surfaces over long distances depends on the shape of the surface. Therefore, the landscape shape is a factor in combating outdoor noise. It is well known that the effect of a hard flat surface can be modeled using two sources: the main source which is located above the surface and its mirror image which is located below the surface. However, if the surface undulates then more fictitious sources are needed to model the surface. In this paper, we propose a method to model rough hard surfaces using equivalent sources which are placed at various distances from the main source in the x-direction. We formulate a method to compute the hard-surface modeled by a multiple-source perturbation of the two equivalent sources. We also used the equivalent source method to model four different surface geometries: a flat, surface with a hill, surface with a hill and valley and undulating surface.