EFFECTS OF GEOMETRY ON THE RESONANCE FREQUENCY OF HELMHOLTZ RESONATORS

An equation for the resonance frequency of a Helmholtz resonator was developed from the wave equation for the case of a cavity volume that was a rectangular parallelepiped and an orifice the Row from which had a constant velocity profile. The development resulted in an explicit form for the interior end correction that included the influence of cavity and orifice geometry. Mean flow across the orifice was not examined. Results for circular, rectangular and cross-shaped orifices were obtained. The results were compared with those from the Rayleigh equation and with those from the transcendental resonance equation, under extremes of orifice and cavity geometry, and orifice position. Both classical equations were found to have constraints on their region of validity when extremes of geometry were encountered. Validity was greatest for a nearly cubical cavity.