Oscillation thresholds for "strinking outwards" reeds coupled to a resonator

Details Oscillation thresholds for "strinking outwards" reeds coupled to a resonator Oscillation thresholds for "strinking outwards" reeds coupled to a resonator

2007-05-29

arxiv.org/abs/0705.4242v1

Physics

Classical Physics

Scientific paper

This paper considers a "striking outwards" reed coupled to a resonator. This expression, due to Helmholtz, is not discussed here : it corresponds to the most common model of a lip-type valve, when the valve is assumed to be a one degree of freedom oscillator. The presented work is an extension of the works done by Wilson and Beavers (1974), Tarnopolsky (2000). The range of the playing frequencies is investigated. The first results are analytical : when no losses are present in the resonator, it is proven that the ratio between the threshold frequency and the reed resonance frequency is found to be necessarily within the interval between unity and the square root of 3. This is a musical sixth. Actually the interval is largely smaller, and this is in accordance with e.g. the results by Cullen et al.. The smallest blowing pressure is found to be directly related to the quality factor of the reed. Numerical results confirm these statements, and are discussed in comparison with previous ones by Cullen et al (2000).

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