Abstract
Helmholtz resonators are widely used, but classical models for the resonators, such as the lumped-element equivalent circuit, are inaccurate for most geometries. This article presents higher-order equivalent circuits for describing the resonators based on the one-dimensional wave equation. Impedance expressions are also derived. These circuits and expressions are given for various constituent resonator components, which may be combined to model resonators with curved, tapered, and straight necks. Resonance frequency predictions using this theory are demonstrated on two realistic resonators. The higher-order predictions are also applied to the theory of side branch attenuators in a duct and the theory of resonator coupling with a mode of an enclosure.
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