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Acoustic Impedance of Outlet of a Hard-Walled Unbaffled Cylindrical Duct for Multimode Incident Wave

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Jurkiewicz J., Snakowska A., Smolik D.
Acta Physica Polonica A
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2011
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vol. 119
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issue 6A
1061-1067
EN
In the paper, the specific acoustic impedance of outlet of an unbaffled duct for incident wave composed of one or many circumferential cut-on duct modes has been derived and presented on graphs. When considering the multimode excitation the equal energy per mode principle and random phases have been assumed. Experimentally verified assumption on equal energy per mode allows for quantitative analysis of the sound field and thus provides more physical insight into the in-duct and out-duct phenomena. The assumption of random phase was implemented by means of the Monte Carlo method and so the expected value, the standard deviation and the percentile curves of the impedance were presented. Numerical data obtained according to the derived theoretical formulae for single and multimode incident wave manifest strong modal character and dependence on the modes phases. The assumption of multimode incident wave has brought the theoretical model closer to what is being observed in practice, especially when ducts of large radius, such as heating and air conditioning systems or turbojet engines, are considered.
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Open End Correction for Arbitrary Mode Propagating in a Cylindrical Acoustic Waveguide

100%
Snakowska A., Jurkiewicz J., Smolik D.
Acta Physica Polonica A
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2011
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vol. 120
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issue 4
736-739
EN
The paper presents a method of theoretical derivation and numerical calculation of the open-end correction coefficient for an arbitrary cut-on mode propagating in acoustic waveguide. Actually, the so-called open-end correction coefficient of acoustic tube, frequently discussed in literature, refers to specific conditions, when the wave heading the outlet is the plane wave. It follows from the fact that the plane wave is a commonly applied approximation when considering phenomena in duct-like devices or systems (tubes, musical instruments, heating or ventilation systems). The aim of the paper is to extend the concept of the open-end correction on the so-called higher Bessel modes, that under some conditions can also propagate in a duct. Theoretical results, forming the basis for numerical calculations, were obtained by considering diffraction at the duct end and applying the Wiener-Hopf factorization method. As a result, the formula for the acoustic field inside the duct was derived. For each Bessel mode present in the incident wave the reflected wave is composed of all cut-on modes of the same circumferential order. Each mode present in the reflected wave is characterized by the complex reflection/coupling coefficient, argument of which describes phase change at the duct end and therefore the open-end correction coefficient can be attributed to each coupled pair of modes.
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