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On the short-wave asymptotic solution of a problem in acoustic radiation

Published online by Cambridge University Press:  24 October 2008

F. G. Leppington
F. G. Leppington
Affiliation:
Department of Mathematics, Imperial College, London
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Abstract

A study is made of a problem in acoustic radiation, with the object of developing a rigorous theory of short-wave asymptotic solutions of the Helmholtz wave equation. The particular example under consideration is that of the radiation of sound waves by a smooth convex cylinder pulsating with prescribed normal velocity V(s) exp (−iωt), where s denotes arc length of the curve C bounding the cylinder cross-section, and ω is the radian frequency.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 64 , Issue 4 , October 1968 , pp. 1131 - 1150
Copyright
Copyright © Cambridge Philosophical Society 1968

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References

REFERENCES

(1)Babich, V. M.Soviet Physics Dokl. 7 (1963), 792.Google Scholar
(2)Goodrich, R. F. and Kazarinoff, N. D.Proc. Cambridge Philos. Soc. 59 (1963), 167.CrossRefGoogle Scholar
(3)Grimshaw, R.Comm. Pure Appl. Math. 19 (1966), 167.CrossRefGoogle Scholar
(4)Kazarinoff, N. D. and Ritt, R. K.IRE Trans. AP-7 (1959), S 21.Google Scholar
(5)Keller, J. B., Lewis, R. J. and Seckler, B. D.Comm. Pure. Appl. Math. 9 (1956), 207.CrossRefGoogle Scholar
(6)Leppington, F. G.Quart. J. Mech. Appl. Math. 20 (1967), 107.CrossRefGoogle Scholar
(7)Leppington, F. G.J. Inst. Math. Appl. 3 (1967), 388.CrossRefGoogle Scholar
(8)Levy, B. R.J. Math. Mech. 9 (1960), 147.Google Scholar
(9)Mikhlin, S. G.Integral equations (Pergamon, 1957).CrossRefGoogle Scholar
(10)Olver, F. W. J.Philos. Trans. Roy. Soc. London, Ser. A 247 (1954), 307, 328.Google Scholar
(11)Sharples, A.Quart. J. Mech. Appl. Math. 20 (1967), 365.CrossRefGoogle Scholar
(12)Ursell, F.Proc. Cambridge Philos. Soc. 53 (1957), 115.CrossRefGoogle Scholar
(13)Ursell, F.Proc. Cambridge Philos. Soc. 62 (1966), 227.CrossRefGoogle Scholar
(14)Ursell, F.Proc. Cambridge Philos. Soc. 64 (1968), 171.CrossRefGoogle Scholar
(15)Watson, G. N.Proc. Roy. Soc. Ser. A 95 (1919), 83.Google Scholar
(16)Ludwig, D.Comm. Pure Appl. Math. 20 (1967), 103.CrossRefGoogle Scholar