A Comparison Between Two and Three-Dimensional Simulations of Finite Amplitude Sound Waves in a Trumpet

Abstract

Simplifying a three-dimensional problem of simulating sound propagation in musical instruments is frequently done by exploiting axial symmetry and reducing the problem to one or two dimensions. We examine if such dimension reduction is valid. We numerically solve the equations of motion of compressible gases using the discontinuous Galerkin method to model nonlinear sound propagation inside a trumpet. The numerical results in two and three dimensions are then compared with experimental data. Experiments were carried out on a trumpet in which the sound pressure waves of the B ₃ ^b and B ₄ ^b notes played at forte were recorded. We found that it is crucial to consider the problem with all three spatial dimensions to ensure reflections in the bell region are properly modelled. Additionally, the shape of flare must be carefully approximated to compute the propagating waves accurately.