@ARTICLE{Meissner_Mirosław_Effect_2010,
 author={Meissner, Mirosław},
 volume={vol. 35},
 number={No 3},
 journal={Archives of Acoustics},
 pages={421-435},
 howpublished={online},
 year={2010},
 publisher={Polish Academy of Sciences, Institute of Fundamental Technological Research, Committee on Acoustics},
 abstract={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.},
 type={Artykuły / Articles},
 title={Effect of Cross-Sectional Area Discontinuities in Closed Hard-Walled Ducts on Frequency of Longitudinal Modes},
 URL={http://www.czasopisma.pan.pl/Content/107547/PDF/91.pdf},
 doi={10.2478/v10168-010-0034-0},
 keywords={longitudinal duct modes, discontinuity in duct cross-section, contraction ratio},
}