Archives of Acoustics, 35, 3, pp. 421–435, 2010

Effect of cross-sectional area discontinuities in closed hard-walled ducts on frequency of longitudinal modes

Mirosław MEISSNER
Institute of Fundamental Technological Research Polish Academy of Sciences

A simple analytical method is developed to estimate frequencies of longitudinal modes in closed hard-walled ducts with discontinuities in a cross-sectional area. The approach adopted is based on a general expression for the acoustic impedance for a plane wave motion in a duct and conditions of impedance continuity at duct discontinuities. Formulae for mode frequencies in a form of transcendental equations were found for one, two and three discontinuities in a duct cross-section. An accuracy of the method was checked by a comparison of analytic predictions with calculation data obtained by use of numerical implementation based on the forced oscillator method with a finite difference algorithm.
Keywords: longitudinal duct modes; discontinuity in duct cross-section; contraction ratio
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