On the Helmholtz resonator

This paper develops the theory of the excitation of a Helmholtz resonator by external disturbances located arbitrarily close to the mouth of the resonator. The classical approach of Rayleigh is thereby extended to situations in which the disturbance at the mouth is not necessarily equivalent to a uniform, time dependent pressure perturbation. The analysis involves the derivation of the Green function of the resonator in a manner similar to that described in an earlier paper. The use of the Green function is illustrated by two examples in which the resonator is excited by a low Mach number stream of air. In the first case the air stream has a periodic large scale structure such as may be caused by a Kelvin-Helmholtz type of instability. The second example models the case of excitation by a shear layer possessing a continuous spectrum of turbulent eddies. In both of these applications the orders of magnitude of the sound pressure levels involved are illustrated for a typical resonator.