The effect of the size of the opening on the acoustic power radiated by a reed woodwind instrument

International audienceFor a given note, the maker of woodwind instruments can choose between different sizes for thetoneholes under the condition that the location is appropriate. The present paper aims at analyzing the consequences of this choice on the power radiated by a hole, which depends on the coupling between the acoustic resonator and the excitation mechanism of the self-sustained oscillation, thus on the blowing pressure. For that purpose a simplifiedreed instrument is investigated, with a cylindrical pipe and a uniqueorifice at the pipe termination. The orifice diameter was varied between the pipe diameter and a size such that the instrument did not play. The pipe length was in each case adjusted to keep the resonance frequency constant. A simple analytical model predicts that, for a given mouth pressure of the instrumentalist, the radiated power does notdepend on the size of the hole if it is wide enough and if resonatorlosses are ignored. Numerical solution of a model including losses confirms this result: thedifference in radiated power between two diaphragm sizes remains smaller than the differenceobtained if the radiated power would be proportional to the orifice cross section area. This is confirmed by experiments using an artificial mouth, but the results show that the linear losses are underestimated, and that significant nonlinear losses occur. Themeasurements are limited to the acoustic pressure at a given distance of theorifice. Experiments also show thatrounding edges of the orifice reduces nonlinear losses resulting in an increase of the powerradiated and of the extinction threshold, and resulting in a larger dynamical range