Broadband acoustic scattering with modern aesthetics from random 3D terrain surfaces generated using the Fourier Synthesis algorithm

Acoustic diffusers are designed to scatter sound to create diffuse sound fields, ideally providing a uniform acoustic experience over a broad frequency range within a listening space. Standard diffuser designs, such as Schroeder diffusers, while effective, may be considered by some to have a design aesthetic that does not conform to particular architectural styles. In this paper the Fourier Synthesis algorithm for procedural 3D random terrain generation is investigated as an alternative for diffuser surface geometry, providing scattering in two dimensions, and scope to vary the bandwidth through a surface smoothness parameter. The scattering properties of a prototype diffuser are investigated experimentally and through numerical modelling using a boundary element method (BEM) program called FastBEM. Good agreement between these is achieved, providing solid validation of the numerical model from which the performance of the diffuser can be assessed. The scattering properties are quantified using polar plots, 3D plots, and the diffusion coefficient. As expected, the Fourier Synthesis diffuser provides good diffusion when the wavelength of the incident sound is comparable to the wavelength of periodicity of the diffuser geometry. A preliminary investigation into the performance of the diffuser for various levels of surface roughness is made, showing that high diffusion can be extended to higher frequencies by increasing the surface roughness of the diffuser.