Computational study of head geometry effects on sound pressure gradient with applications to head-related transfer function

Abstract

Effects of object geometry on sound scattering of far-field incident sound waves for two different head models (spherical and ellipsoidal) have been studied using an optimized Finite Element Method (FEM) based on frequency-dependent adaptive dimensions. This optimized FEM technique is proven both efficient and accurate when compared with analytical results for the spherical model, with maximum deviation of 0.6 dB. Comparisons between models have been made on the equivalent Head-Related Transfer Functions (HRTFs) for acoustic pressure, and for the first and second order pressure gradients on the surface. It is shown that while directionality cannot be achieved at lower frequencies using only pressure, pressure gradients provide sound cancellation for certain source orientations. Hence, it is possible to cancel incoming sound from the front (or behind) or sides depending on the direction (radial, azimuthal) and order of pressure gradients. While the pattern of pressure gradient directionality remains similar between the spherical and ellipsoidal models, the difference in dimensions affects the amplitude of the equivalent HRTFs for these parameters. This study provides insight into the placement of directional microphones on the head for hearing aids.