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The refraction of sound pulses

Published online by Cambridge University Press:  24 October 2008

Roger Grimshaw
Roger Grimshaw
Affiliation:
University of Melbourne
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Abstract

The problem considered is that of the diffraction of sound pulses by a plane interface separating two stratified media in each of which the refractive index increases with distance from the interface. Two types of diffraction phenomena occur, glancing ray diffraction and total reflection. The solution is obtained as a series of ‘pulse propagation modes’, using a double transform technique. The main results are some formulae for the pulse field near a diffracted wavefront.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 4 , October 1967 , pp. 1247 - 1272
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

REFERENCES

(1)Brekhovskikh, L. M.Waves in layered media (Academic Press, N.Y., 1960).Google Scholar
(2)Chester, C. R. and Keller, J. B.Research Report No. EM-150, Inst. of Math. Sci. (New York University, 1959).Google Scholar
(3)Coddington, E. A. and Levinson, N.Theory of ordinary differential equations (McGraw-Hill, N.Y., 1955).Google Scholar
(4)Doetsch, G.Einführung in Theorie und Anwendung der Laplace-Transformation (Birkhäuser-Verlag, Basel 1958).Google Scholar
(5)Erdélyi, A. et al. Tables of integral transforms, vol. 1 (McGraw-Hill, N.Y. 1954).Google Scholar
(6)Friedlander, F. G.Proc. Cambridge Philos: Soc. 45 (1949), 395.Google Scholar
(7)Friedlander, F. G.Comm. Pure Appl. Maths. 7 (1954), 705.CrossRefGoogle Scholar
(8)Friedlander, F. G.Research Report No. EM-76, Inst. of Math. Sci. (New York University, 1955).Google Scholar
(9)Friedlander, F. G.Sound pulses (Cambridge University Press, 1958).Google Scholar
(10)Friedman, B.Principles and techniques of applied mathematics (John Wiley and Sons, N.Y., 1956).Google Scholar
(11)Garnir, H. G.Bull. Soc. Roy. Sci. Liège 22 (1953), 85, 148.Google Scholar
(12)Gilbert, F.J. Acoust. Soc. Amer. 32 (1960), 841.Google Scholar
(13)Gilbert, F. and Knopoff, L.J. Acoust. Soc. Amer. 31 (1959), 1169.Google Scholar
(14)Gilbert, F. and Knopoff, L.Bull. Siesmol. Soc. Amer. 51 (1961), 35.Google Scholar
(15)Grimshaw, R.Proc. Cambridge Philos. Soc. 60 (1964), 1013.Google Scholar
(16)Grimshaw, R. Ph.D. Thesis, Cambridge University (1964).Google Scholar
(17)Jones, D. S.Phil. Trans. (London) 225 A (1963), 341.Google Scholar
(18)Jones, D. S.The theory of electromagnetism (Pergamon Press, Oxford, 1964).Google Scholar
(19)Keller, J. B.J. Appl. Phys. 25 (1954), 938.CrossRefGoogle Scholar
(20)Keller, J. B. and Lewis, R. M.Research Report No. EM-194, Inst. of Math. Sci. (New York University, 1964).Google Scholar
(21)Levy, B. R. and Keller, J. B.Comm. Pure Appl. Maths. 12 (1959), 159.CrossRefGoogle Scholar
(22)Mishra, S. Ph.D. Thesis, Cambridge University (1961).Google Scholar
(23)Mishra, S.Proc. Cambridge Philos. Soc. 60 (1964), 295.CrossRefGoogle Scholar
(24)Olver, F. W. J.Phil. Trans. (London) 247 A (1954), 307, 328.Google Scholar
(25)Ragab, F. M.Comm. Pure Appl. Maths. 11 (1958), 115.Google Scholar