A Two-Dimensional Study of Finite Amplitude Sound Waves in a Trumpet Using the Discontinuous Galerkin Method

Abstract

A model for nonlinear sound wave propagation for the trumpet is proposed. Experiments have been carried out to measure the sound pressure waveforms of the [Formula: see text] and [Formula: see text] notes played forte. We use these pressure measurements at the mouthpiece as an input for the proposed model. The compressible Euler equations are used to incorporate nonlinear wave propagation and compressibility effects. The equations of motion are solved using the discontinuous Galerkin method (DGM) and the suitability of this method is assessed. The third spatial dimension is neglected and the consequences for such an assumption are examined. The numerical experiments demonstrate the validity of this approach. We obtain a good match between experimental and numerical data after the dimensionality of the problem is taken into account.