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Expansion chambers are widely used in the breathing systems of engines due to their desirable broadband noise attenuation characteristics. Following an earlier analytical and computational work of Sahasrabudhe et al. (1992), the present study investigates the effect of the length on the acoustic attenuation performance of concentric expansion chambers. Three approaches are employed to determine the transmission loss: (1) a two-dimensional, axisymmetric analytical solution; (2) a three-dimensional computational solution based on the boundary element method; and (3) experiments on an extended impedance tube setup with nine expansion chambers fabricated with fixed inlet and outlet ducts, fixed chamber diameters, and varying chamber length to diameter ratios from to 3.53. The results from all three approaches are shown to agree well. The effect of multi-dimensional propagation is discussed in comparison with the classical treatment for the breakdown of planar waves.

Helmholtz resonators are widely used for noise reduction in vehicle induction and exhaust systems. This study investigates the effect of specific cavity dimensions of these resonators theoretically, computationaly, and experimentally. An analytical model is developed for circular concentric resonators to account for the multidimensional wave propagation in both the neck and the cavity. Driving this model with an oscillating piston isolates the interface between the neck and the resonator volume, thereby allowing, at this location, for an accurate evaluation of the empirical end correction, which is often used with the classical lumped approach in an attempt to incorporate the effect of multidimensional behavior at the transitions. The analytical method developed in the study is then compared with a similar one-dimensional analytical model that also allows for wave propagation in the neck and cavity.