Modeling free reed behavior using calculated reed admittance

Abstract

For musical wind instruments driven by a reed mechanism, Fletcher has provided an analysis which shows that a necessary condition for the sounding of an instrument is that the acoustic admittance of the reed has a real part, which is negative and greater in magnitude than the real part of the pipe admittance [N. H. Fletcher, Acustica 43, 63–72 (1979)]. The analysis also shows that inward-striking (closing) and outward-striking (opening) reeds will exhibit different behavior. Free reeds, used in instruments such as the reed organ, harmonica, accordion, and the Asian free reed mouth organs, can exhibit behavior characteristic of either opening or closing reeds, depending on the details of the configuration. Using reed parameters determined by experiment, the reed admittance as a function of frequency has been calculated for free reeds and used to make quantitative predictions. For a variety of free-reed parameters, the frequency of vibration as a function of blowing pressure has been calculated and compared with experimental results. Cases are considered in which a reed is coupled to a pipe resonator as well as cases in which the reed is not coupled to a resonator.