Fluid mechanical model of the Helmholtz resonator

A semi-empirical fluid mechanical model of the acoustic behavior of Helmholtz resonators is presented which predicts impedance as a function of the amplitude and frequency of the incident sound pressure field and resonator geometry. The model assumes that the particle velocity approaches the orifice in a spherical manner. The incident and cavity sound fields are connected by solving the governing oscillating mass and momentum conservation equations. The model is in agreement with the Rayleigh slug-mass model at low values of incident sound pressure level. At high values, resistance is predicted to be independent of frequency, proportional to the square root of the amplitude of the incident sound pressure field, and virtually independent of resonator geometry. Reactance is predicted to depend in a very complicated way upon resonator geometry, incident sound pressure level, and frequency. Nondimensional parameters are defined that divide resonator impedance into three categories corresponding to low, moderately low, and intense incident sound pressure amplitudes. The two-microphone method was used to measure the impedance of a variety of resonators. The data were used to refine and verify the model.