An analytical solution for a low barrier in a turbulent atmosphere

Other conference contribution, 2005

Buildings and other kinds of sound barriers are commonly used to reduce traffic noise. Atmospheric turbulence causes scattering of sound into the shielded zones created by barriers. The sound level increase is expected to be significant usually for large geometries, and at higher frequencies. For steep geometries, i.e. with a high barrier close to the source or to the receiver, a scattering cross section based model can be used to predict the increase in sound level. Here, another approach is used, which is applicable to flat geometries, i.e. where the barrier is low in comparison to its distance to both the source and the receiver. The work is based on a previously developed substitute sources method (SSM). A two-dimensional modelling is done and no ground surface is considered. To numerically solve the full SSM formulation of the problem is computationally demanding due to a double integral. To reduce the computational cost, an analytical solution is derived. As an intermediate step an expression containing a single integral is found, which enables a numerically fast method. The full SSM formulation is used as reference, and agreement between the SSM and the fast method is reasonably good. The analytical solution involves further approximations and has a smaller range of validity than the fast method. Additional restraints are formulated for the applicability of the analytical solution.