# Ursi Undergraduate Research Summer Institute

Physics
Completed Project

## Numerical Prediction of Sound Scattering From Fractal Surfaces

Mallory Morgan, Vassar College ’17, Samuel Gilbert, Vassar College ’18 and Profs. David T. Bradley and Feruza Amirkulova
Diffusers are reflecting surfaces with non-planar geometries that ideally disperse sound uniformly in all directions. The uniformity of this reflected sound dispersion is dependent on the relative size of the surface geometry features with respect to the wavelength of the incident sound. The diffusion coefficient is one quantifier of this dispersion, which is referred to as sound scattering. The polar response is another quantifier that provides a more qualitative indicator of sound scattering based on a visual analysis of the response. A broad frequency range of scattering is needed in acoustically sensitive spaces because the human ear is sensitive across a broad frequency range. Fractal diffusers can theoretically provide such scattering because their geometry is self-similar across different scales. In this project, the diffusion coefficient and polar response plots of virtually generated fractal surfaces were numerically simulated using the Boundary Element Method (BEM). In this analysis technique, a system of partial integral equations is formulated and solved computationally to determine the sound pressures on and near the surfaces. Two software packages were used to carry out this analysis: MATLAB and AcouSTO. In addition to varying the software package used for the simulations, the method of surface remeshing and several parameters of the fractal generation algorithm were also varied to study their effect on the data. In the future, the virtually generated surfaces will be physically created using a 3-D printer, and the scattering behavior of the surfaces will be experimentally measured, which will allow for the verification of the simulations’ accuracy.