The effect of the size of an opening on the acoustic power produced by a woodwind instrument
Résumé
When designing a woodwind instrument, for a given playing frequency, themaker can choose between a large range of sizes and locations for thetoneholes. The present paper aims at analyzing the consequences of thischoice 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 simplifiedproblem is investigated: that of a reed cylindrical pipe with a uniqueorifice at the end. The orifice diameter was varied from the pipe diameter down to 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 analytic model shows that, for a given mouth pressure of the instrumentalist, the radiated power does notdepend on the size of the hole if the hole is wide enough and if resonatorlosses are ignored. Numerical computation confirms this result, and allowsexhibiting the effect of losses: their effect is not negligible, but 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 amount of linear losses is underestimated by the models, and that significant nonlinear losses occur. Themeasurement is limited to the acoustic pressure at a given distance of theorifice (assuming a monopole radiation). Experiments also show thatrounding edges of the hole leads to an increase of the powerradiated and of the extinction threshold, therefore of the dynamic range.
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