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.
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Selamet et al. (1994) studied this question.
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