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2011 | 120 | 4 | 736-739
Article title

Open End Correction for Arbitrary Mode Propagating in a Cylindrical Acoustic Waveguide

Content
Title variants
Languages of publication
EN
Abstracts
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.
Keywords
EN
Publisher

Year
Volume
120
Issue
4
Pages
736-739
Physical description
Dates
published
2011-10
Contributors
author
  • Faculty of Mechanical Engineering and Robotics, AGH, al. A. Mickiewicza 30, 30-059 Cracow, Poland
author
  • Faculty of Electrical Engineering, Automatics, IT and Electronics, AGH, al. A. Mickiewicza 30, 30-059 Cracow, Poland
author
  • Faculty of Physics and Applied Computer Science, AGH, 30-059 Cracow, Poland
References
  • 1. E. Skudrzyk, The Foundations of Acoustics, Springer-Verlag, Wien 1971
  • 2. A. Snakowska, Acoustic Field Analysis of Cylindrical Waveguide with Concerning of Diffraction Effects on the Outlet, Publishers of Rzeszów University, Rzeszów 2007 (in Polish)
  • 3. S. Lidoine, H. Batard, S. Troyes, A. Delnevo, M. Roger, in: AIAA-2001-2140 AIAA/CEAS Aeroacoustics Conference and Exhibit, 7th, Maastricht 2001, Collection of Technical Papers 1, AIAA, Maastricht 2001
  • 4. A. Snakowska, J. Jurkiewicz, Acta Acustica/Acustica 96, 416 (2010)
  • 5. P. Joseph, P.A. Nelson, M.A. Fisher, J. Acoust. Soc. Am. 106, 766 (1999)
  • 6. A. Snakowska, R. Wyrzykowski, Archiv. Acoust. 11, 261 (1986)
  • 7. A. Snakowska, H. Idczak, Acta Acustica 3 119 (1995)
  • 8. L.A. Weinstein, The theory of diffraction and the factorization method, Golem Press, Boulder (Co) 1969
  • 9. B. Rayleigh, Theory of Sound, Dover, New York 1945
  • 10. H. Levine, J. Schwinger, Phys. Rev. 73, 383 (1948)
  • 11. Y. Nomura, I. Yamamura, S. Inawashiro, J. Phys. Soc. Jpn. 15, 510 (1960)
  • 12. Y. Ando, Acustica 22, 219 (1969)
  • 13. M. Peters, A. Hirschberg, A. Reijnen, A. Wijnands, J. Fluid Mech. 256, 499 (1993)
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.bwnjournal-article-appv120n437kz
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