Reed Instruments, from Small to Large Amplitude Periodic Oscillations and the Helmholtz Motion Analogy

Jean-Pierre Dalmont (1) , Joël Gilbert (1) , Jean Kergomard (1)

1 LAUM - Laboratoire d'Acoustique de l'Université du Mans

When studying the oscillations of reed instruments different approaches and simplifications can be used to understand the behaviour of such instruments. Two theoretical approaches were successfully used by previous authors. The first one consists in analysing the small oscillations near the threshold. The second one, applied until now only on cylindrical resonators, analyses the squared oscillations with a loss less model of the resonator. The aim of this paper is on one hand to apply the lossless analysis to conical like instruments and on the other hand to try to understand how the small oscillations model matches with the lossless model. In this study the cone is replaced by resonators which are known to be approximately equivalent and for which the input impedances allow analytical developments. Differences in behaviour between cylinders and cones are demonstrated. Contrary to cylindrical instruments, for conical instruments there is a subcritical threshold and no small amplitude oscillations. Moreover, there is more than one regime at the fundamental frequency in conical instruments. Two of these, similar to the Helmholtz motions in bowed string instruments are studied in this paper. Theoretical results are qualitatively compared with experiments using a blowing machine.

Domaines: Acoustique [physics.class-ph]; Acoustique [physics.class-ph]

Jean-Pierre Dalmont, Joël Gilbert, Jean Kergomard. Reed Instruments, from Small to Large Amplitude Periodic Oscillations and the Helmholtz Motion Analogy. Acta Acustica united with Acustica, 2000, 86 (4), pp.671-684. ⟨hal-00474996⟩