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Helmholtz resonators are widely used for the noise reduction in vehicle induction and exhaust systems. This study investigates the effect of specific cavity dimensions of these resonators theoretically, computationally and experimentally. By considering one-dimensional wave propagation through distributed masses in the connector and cavity, a closed-form expression for the transmission loss of axisymmetric configurations is presented, thereby partially eliminating the limitations of a lumped-parameter analysis. Eight resonators of fixed neck geometry and cavity volume with length-to-diameter ratios of the volume varying from 0.32 to 23.92 are studied both computationally and experimentally. The first of the two computational approaches employed in the study implements a finite difference time domain technique to solve the nonlinear governing equations of one-dimensional compressible flow.

A time-domain computational approach is applied to analyze the acoustic performance of multiple-pass silencers containing perforated tube sections. The nonlinear, one-dimensional method may readily include temporal and spatial variations in sound pressure level, orifice flow velocities, and mean duct flow, all of which affect the behavior of perforated tube elements. The transmission loss characteristics of two anechoically-terminated multiple pass muffler configurations are determined computationally and experimentally for the limiting case of low sound pressure levels and zero mean flow. Comparisons between the numerical results and experimental data are shown to correlate well for frequencies where the one-dimensional assumption is justified.