Aix Marseille Univ, CNRS, Centrale Marseille, LMA, UMR 7031, Marseille
The input impedance is a useful quantity to characterize the acoustic response of woodwind instruments and is efficiently simulated using the Transfer Matrix Method (TMM). However, the TMM does not calculate intermediate variables that are convenient for simulating the external sound field. Recent work by Lefebvre et al proposes the Transfer Matrix Method with external Interactions (TMMI) which accounts for the mutual radiation impedance of toneholes radiating into the same space and uses the acoustic flow through each aperture as the reference variable. Treating the flow through each tonehole as a source in a linear array, it is possible to calculate the external sound field such as the waveforms at a given receiver location and directivity patterns. Additionally, the efficiency of a resonator can be calculated as the ratio of the power at the input of the resonator and the sum of the power radiating from each aperture. This is a useful step towards understanding the competition between the energy that is retained within a resonator and facilitates the auto-oscillation of the reed, and that which radiates from the resonator. This topic is explored through simulation and measurements using simplified cylindrical resonators.
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