Comparisons between models and measurements of the input impedance of brass instruments bells

This work is part of a project aiming at helping craftsmen to design and characterize their musical instruments. Starting from a given wind instrument shape, our objective consists in choosing the most relevant physical model able to predict the acoustical input impedance of this musical instrument once constructed. The modeling of bells in brass instruments is still problematic as the limits of plane wave approximation are known but no method is proven to give accurate results. The aim of the present paper is to compare the results given by di erent methods with measurements. Four di erent bells with known geometries are used in this study. These bells input impedances are calculated with a Boundary Element Method and with Transmission-Matrix Methods loaded with various radiation impedance models and based on axial or curvilinear abscissa. Surprisingly, a simple 1D wave propagation approximation based on curvilinear abscissa coupled with the radiation impedance of a pulsating portion of sphere gives results very close to the measurement. PACS no. 43.75.Fg, 43.20.Mv