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

Abstract For a given note, the maker of woodwind instruments can choose between different sizes for the toneholes 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 simplified reed instrument is investigated, with a cylindrical pipe and a unique orifice 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 not depend on the size of the hole if it is wide enough and if resonator losses are ignored. Numerical solution of a model including losses confirms this result: the difference in radiated power between two diaphragm sizes remains smaller than the difference obtained 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. The measurements are limited to the acoustic pressure at a given distance of the orifice. Experiments also show that rounding edges of the orifice reduces nonlinear losses resulting in an increase of the power radiated and of the extinction threshold, and resulting in a larger dynamical range.