Resonance frequencies and sound absorption of Helmholtz resonators with multiple necks

Abstract

A new analytical model is proposed to calculate the resonance frequency and the input impedance of a Helmholtz resonator with multiple necks. Such resonators occur in practice, for example, when leaks are introduced as additional necks inside the wall of the resonators. The model uses a lumped representation of the air volumes enclosed by the necks to derive an explicit formula for the resonance frequency. Using this formula, it can be explained that the low reactance of the air volumes inside leaks of thin-walled Helmholtz resonators leads to the strong increase of the resonance frequency, as observed in previous studies. The results of the analytical model are validated with the help of experimental data available in the literature and impedance tube measurements. The analytical model as well as the measurements clearly show, that even small holes in the Helmholtz resonator lead to a significant increase in the resonance frequency and the absorption performance can be considerably reduced. The simple model can be applied to design Helmholtz resonators with multiple necks or estimate the impact of leaks.