A general expression for the transmission loss characteristics of the Herschel-Quincke tube is developed. This relationship eliminates the restrictions on duct cross-sectional area employed in earlier analytical studies. The attenuation of sound by this configuration is also studied computationally in terms of a nonlinear one-dimensional finite-difference model that solves the balance equations of mass, momentum, and internal energy, coupled with the ideal gas equation of state. Transmission loss predictions from both analytical and computational models are then shown to correlate well with experimental data ,acquired from an extended impedance tube setup. INTRODUCTION The Herschel-Ouincke tube is a parallel connection of two pipes having arbitrary lengths and constant, although not necessarily equal, cross-sectional areas. Studies of this configuration date back to Herschel and Quincke's attempts in the 19th century, and Stewart's refinement early in the 20th century (Herschel, 1833; Quincke, 1866; Stewart, 1928; Stewart and Lindsay, 1930). Since then, the configuration has received relatively little attention [see, for example, the classic NACA report (Davis et aL, 1954) for a brief mention and 3177 d. Acoust. Soc. Am. 96 (5), Pt.

The effect of specific cavity dimensions of circular concentric Helmholtz resonators is investigated theoretically, computationally, and experimentally. Three analytical models are employed in this study: (1) A two-dimensional model developed to account for the nonplanar wave propagation in both the neck and the cavity; (2) a one-dimensional solution developed for the limit of small cavity length-to-diameter ratio, l/d, representing a radial propagation in the cavity; and (3) a one-dimensional closed-form solution for configurations with large l/d ratios which considers purely axial wave propagation in the neck and the cavity. For low and high l/d, the resonance frequencies determined from the two-dimensional approach are shown to match the one-dimensional predictions. For cavity volumes with l/d>0.1, the resonance frequencies predicted by combining Ingard’s end correction with one-dimensional axial wave propagation are also shown to agree closely with the results of the two-dimensional model. The results from the analytical methods are then compared with the numerical predictions from a three-dimensional boundary element method and with experiments. Finally, these approaches are employed to determine the wave suppression performance of circular Helmholtz resonators in the frequency domain.

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A time-domain computational approach is applied to investigate the behavior of perforated tube silencers at high sound levels. The one-dimensional computational technique employs a lumped parameter model for the perforate flows. The lumped parameter perforate model is based on time-invariant approximations for the equivalent length l(eq) and resistance R, consistent with the use of a nonlinear perforate impedance. Empirical expressions for l(eq) and R are developed experimentally using nondimensional scaling parameters. The model is applied to geometries representative of automotive resonators and multiple-duct mufflers. Conditions are simplified from those in an actual automotive system by considering single-frequency excitation and zero mean flow. Simulations with linear perforate behavior are compared to experimental data obtained with an extended impedance tube system. Simulations with nonlinear perforate behavior for one concentric tube resonator are compared to published experimental data.