Three-dimensional simulations of sound propagation in a trumpet with accurate mouthpiece shank geometry

Abstract: The length and bore geometry of musical instruments directly influences the quality of sound that can be produced. In brass instruments, nonlinear effects from finite-amplitude wave propagation can lead to wave distortion giving sounds a brassy timbre [3, 5, 14, 20, 26]. In this paper, we propose a three-dimensional model to describe nonlinear wave propagation in a trumpet and investigate the importance of the mouthpiece shank geometry. Time pressure waveforms corresponding to B_3(b) and B_4(b) notes were recorded at the mouthpiece shank and used as inputs for our model. To describe the motion of compressible inviscid fluid, we numerically solved the compressible Euler equations using the discontinuous Galerkin method. To validate our approach, the numerical results were compared to the recorded musical notes outside the bell of the trumpet. Simulations were performed on computational trumpets where different bore geometries were considered. Our results demonstrate that the shape of the narrow region near mouthpiece greatly influences the wave propagation and accuracy of the trumpet model.