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Trapped modes in a waveguide with a long obstacle

Published online by Cambridge University Press:  25 January 2000

N. S. A. KHALLAF ,
L. PARNOVSKI  and
D. VASSILIEV
N. S. A. KHALLAF
Affiliation:
University of King Abdulaziz, College of Education, Department of Mathematics, Al-Madinah Al-Munawwarah, PO Box 344, Kingdom of Saudi Arabia Present address: School of Mathematical Sciences, University of Sussex, Brighton BN1 9QH, UK.
L. PARNOVSKI
Affiliation:
School of Mathematical Sciences, University of Sussex, Brighton BN1 9QH, UK
D. VASSILIEV
Affiliation:
Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, UK
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Abstract

Consider an infinite two-dimensional acoustic waveguide containing a long rectangular obstacle placed symmetrically with respect to the centreline. We search for trapped modes, i.e. modes of oscillation at particular frequencies which decay down the waveguide. We provide analytic estimates for trapped mode frequencies and prove that the number of trapped modes is asymptotically proportional to the length of the obstacle.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 403 , 25 January 2000 , pp. 251 - 261
Copyright
© 2000 Cambridge University Press

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