Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-26T08:35:04.964Z Has data issue: false hasContentIssue false
  • English
  • Français

Diffraction by a cylinder of finite length

Published online by Cambridge University Press:  24 October 2008

W. E. Williams  and
M. J. Lighthill
W. E. Williams
Affiliation:
Department of Mathematics*Manchester University
Get access Rights & Permissions [Opens in a new window]

Abstract

The diffraction of a plane harmonic sound wave by a hollow circular cylinder of finite length is considered. The problem is treated by using Laplace transforms and is reduced to the solution of two complex integral equations. An approximate solution is obtained for these equations when the product of the wave number (k) and the cylinder length (l) is large. The resonance of the system is considered and an equation derived for the resonant lengths which is then solved approximately for kl large. An explicit expression is obtained for the end correction of an. r–resonant system (i.e. kl ≈ rπ), and also comparison is made with experimental results.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 52 , Issue 2 , April 1956 , pp. 322 - 335
Copyright
Copyright © Cambridge Philosophical Society 1956

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Anderson, S. H. and Ostensen, F. C.Phys. Rev. (2), 31 (1928), 267.Google Scholar
(2)Erdélyi, A. and Kernack, W. O.Proc. Camb. phil. Soc. 41 (1945), 74.Google Scholar
(3)Jones, D. S.Quart. J. Mech. 3 (1950), 420.CrossRefGoogle Scholar
(4)Jones, D. S.Quart. J. Math. (2), 3 (1952), 189.Google Scholar
(5)Jones, D. S.Phil. Trans. A, 247 (1955), 499.Google Scholar
(6)Levine, H. and Schwinger, J.Phys. Rev. (2), 73 (1948), 383.Google Scholar
(7)Pearson, J. D.Proc. Camb. phil. Soc. 49 (1953), 659.CrossRefGoogle Scholar
(8)Sommerfeld, A.Partial differential equations (New York, 1949).Google Scholar
(9)Watson, G. N.Theory of Bessel functions (Cambridge, 1922).Google Scholar
(10)Whittaker, E. T. and Watson, G. N.Modern analysis (Cambridge, 1902), chap. 16.Google Scholar
(11)Williams, W. E.Proc. Camb. phil. Soc. 50 (1954), 309.Google Scholar