Acoustic performance of a concentric circular Helmholtz resonator with an extended neck is investigated theoretically, numerically, and experimentally. The effect of length and shape of, and the perforations on the neck extension is examined on the resonance frequency and the transmission loss. A two-dimensional analytical method is developed for an extended neck with constant cross-sectional area, while a three-dimensional boundary element method is applied for the variable area and perforated extension. Lumped and one-dimensional approaches are also included to illustrate the effect of the higher order modes. For a piston-driven model, predicted resonance frequencies using lumped, one-dimensional, and two-dimensional analytical methods are compared with those from multidimensional boundary element method. Analytical and computational transmission loss predictions for pipe-mounted model are compared to the experimental data obtained from an impedance tube setup. It is shown that the resonance frequency may be controlled by the length, shape, and perforation porosity of the extended neck without changing the cavity volume.

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A two-dimensional analytical solution is developed to determine the acoustic performance of a perforated single-pass, concentric cylindrical silencer filled with fibrous material. To account for the wave propagation through absorbing fiber and perforations, the complex characteristic impedance, wave number, and perforation impedance are employed. With expressions for the eigenvalues and eigenfunctions of sound propagation in the perforated dissipative chamber, the transmission loss is obtained by applying a pressure and velocity matching technique. The results from the analytical method are then compared with both experiments and numerical predictions based on the boundary element method ͑BEM͒, showing a reasonable agreement. The effects of geometry, fiber properties, and perforation porosity on the acoustic attenuation performance are discussed in detail.