# Dependence of the acoustic power produced by a woodwind on the tonehole size

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* Corresponding author 1 LMA - Laboratoire de Mécanique et d-Acoustique Marseille 2 Sons LMA - Laboratoire de Mécanique et d-Acoustique Marseille

Abstract : It is well known that for a given note the position of woodwind toneholes can be chosen by the maker in a certain portion of the instrument, provided that the radius is properly chosen: a wide radius needs to be located further from the reed than a narrow one. In our work a simplified problem with one radiating source only is investigated: the problem of a short diaphragm at the end of a cylindrical tube, excited by a clarinet-like reed-mouthpiece. We consider tubes of different lengths provided with diaphragms of different radii, in order to keep a fixed playing frequency. Obviously the power radiated by the orifice decreases when the diaphragm radius decreases. But it is not intuitive that when the radius is large enough, the power is found to be almost independent of the radius. Indeed it can be shown that the radiated power depends only on the output flow rate. Moreover energy considerations show that the ratio between the input pressure and the output flow rate does not depend on the length, thus on the diaphragm radius. Finally when losses are ignored, the input pressure depends on the excitation pressure in the mouth but is independent of the tube. At low level of excitation, this simple explanation is confirmed by both numerical calculation and experiment, but experiment confirms the importance of nonlinear effects with flow separation due to sharp corners.

Author: ** A Guilloteau - P Guillemain - J Kergomard - **

Source: https://hal.archives-ouvertes.fr/