PhD Comprehensive Seminar | Janelle Resch, A Three-Dimensional Study of Nonlinear Acoustic Models

A Three-Dimensional Study of Nonlinear Acoustic Models

The amplitude of most audible sound waves is only a small fraction of atmospheric pressure. From a mathematical perspective, this means a small amplitude linearization can be applied to the equations of motion resulting in a linear model. However, to accurately describe the production and propagation of high amplitude sound pressure waves, such an assumption cannot be made. The nonlinear behaviour of the wave propagation becomes evident for waves that have evolved long enough with large enough amplitude. In particular, wave steepening can occur and shock waves may even be generated.

The purpose of this seminar is to examine how one can model sound production and propagation in brass instruments. Linear models are not sufficient for an accurate description and therefore, the equations of motion must be solved numerically (preferably considering all three spatial dimensions). The acoustic community consensus is that shock waves can form in the trombone as well as the trumpet. However, theoretical verification is still needed and there is some debate on which notes predominantly generate shock waves. This seminar will also examine important geometric properties in the simulated model.