Noise attenuation capacity of a Helmholtz resonator

The noise attenuation capacity of a HR defined as the integral of transmission loss in the frequency domain is first derived.The theoretical formula of noise attenuation capacity shows that it is only determined by the geometries of the neck and the cross-sectional area of the duct.The theoretical formula is validated by FEM simulation using COMSOL Multiphysics.The noise attenuation capacity is a significant supplement to theoretical studies and engineering applications of HRs. Helmholtz resonator (HR) is one of the most basic acoustic models and has been widely used in engineering applications due to its simple, tunable and durable characteristics. The transmission loss index is mainly used to evaluate the acoustic transmission performance. Based on the transmission loss index, this paper proposes the noise attenuation capacity index as one of the key parameters to evaluate the noise attenuation performance of a HR. The noise attenuation capacity is defined as the integral of transmission loss in the frequency domain. The theoretical formula of a HR's noise attenuation capacity is first derived in this study. It indicates that the noise attenuation capacity of a HR is only related to geometries of the neck and duct's cross-sectional area. The cavity volume has no effects on its noise attenuation capacity. The proposed theoretical formula of a HR's noise attenuation capacity is validated by Finite Element Method (FEM) simulation using commercial software (COMSOL Multiphysics). The proposed noise attenuation capacity of a HR should therefore be considered as one of the main acoustic characteristics of a HR. It is hoped that the present study could provide a stepping stone for the investigation of the HR's or other silencers noise attenuation capacity and potential applications in all research areas in respect of the HR.

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