Dual Helmholtz resonator

Acoustic characteristics of a dual Helmholtz resonator which consists of a pair of cylindrical neck and cavity connected in series (neck–cavity–neck–cavity) are established primarily in terms of a lumped-parameter theory. The results are then compared to (a) a two-dimensional analytical approach by applying a pressure/velocity matching technique for a piston-driven model; (b) a three-dimensional boundary element method for a pipe-mounted model; and (c) experiments on an impedance-tube test setup with one fabricated prototype installed in a sidebranch orientation (pipe-mounted model). Closed-form expressions have been developed in the present study for the resonance frequencies and the transmission loss of this two degree-of-freedom system based on the Newton’s second law of motion for a lumped system. The resonance frequencies and the transmission loss from this theory agree well with the analytical results, while showing a reasonable comparison with both the numerical predictions and the measurements.