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 [3,5,16,22,29]. 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. The time pressure waveforms corresponding to B3b and B4b notes at the mouthpiece were recorded at the mouthpiece shank are recorded and used as inputs for our model. To incorporate compressibility and nonlinear effects, the compressible Euler equations are used to describe the evolution of the nonlinear waves. The system was solved numerically using the discontinuous Galerkin method. The numerical results were compared with the waveforms of the musical notes, which were also measured outside the bell of the trumpet, to validate our approach. Simulations were run for both notes in computational trumpets where different bore geometries were modelled. Our results demonstrate that the shape of the narrow region near the mouthpiece greatly influences the wave propagation and must be considered in a trumpet model.