Autonomous vibration of simple pressure-controlled valves in gas flows

Pressure-controlled gas-flow valves are responsible for sound generation in woodwind and brass instruments, and in the vocalization of many animals. When only a single degree of freedom is allowed for the valve motion, four simple configurations are possible, depending upon the effect upon the valve opening of static overpressures applied at either inlet or outlet ports in the presence of the flow. It is shown that, depending upon the valve configuration, there exist particular ranges of acoustic impedance for the inlet and outlet ducts to the valve within which self-sustained valve oscillation is possible. The results are particularly simple when the lengths of these ducts are less than one-quarter of a wavelength at the resonant frequency of the valve, in which circumstance oscillation takes place close to that resonance frequency. The analysis treats only the initiation of oscillations of small amplitude, as a precursor to the maintenance of large-amplitude nonlinear oscillations.