The response of Helmholtz resonator to external excitation. Part I: Acoustically induced resonance

Abstract

The first of two companion papers theoretical and experimental results are presented for a Helmholtz resonator subject to external excitation by an acoustic plane wave. The response of the resonator was analysed in terms of the relation between the pressure induced in the interior of the resonator and the driving pressure. Equations for the resonance frequency and the quality factor were developed for the cavity that was a rectangular parallelepiped with a centered circular orifice. The flow from the cavity had a constant velocity profile. The resonator was modelled by an equivalent impedance circuit, predicted from the classic theory of sound radiation, with an additional resistive term connected with the viscous action inside the orifice. The theoretical results were compared with experimental data for a frequency chosen so as to tune the system to the lowest resonance mode. The experiment has shown that the acoustic response of resonator was changed considerably when mechanical vibrations of the resonator elements were excited. A phenomenon of flow-induced resonance in the considered system geometry will be presented in the companion paper.