Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-25T04:50:48.477Z Has data issue: false hasContentIssue false
  • English
  • Français

An approximate method in high-frequency scattering

Published online by Cambridge University Press:  24 October 2008

A. Sharples
A. Sharples
Affiliation:
The UniversityLiverpool
Get access Rights & Permissions [Opens in a new window]

Abstract

The diffraction of a high-frequency plane sound wave by a circular cylinder is investigated when the boundary condition on the cylinder is expressed by means of an equation of the form The special feature of this investigation is that an extended form of the Kirchhoff-Fresnel theory of diffraction is used to find an integral representation for the scattering coefficient. In order to avoid the complicated analysis which would be necessary to evaluate the integrals concerned, the more natural geometrical acoustics approach is used to find the first correction term in the scattering coefficient. Numerical results are given for large and small values of the impedance Z.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 58 , Issue 4 , October 1962 , pp. 662 - 670
Copyright
Copyright © Cambridge Philosophical Society 1962

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)Barakat, R., Math. Comp. 15 (1961), 7.CrossRefGoogle Scholar
(2)Erdélyi, A. et al. , Higher transcendental functions, vol. 1 (McGraw-Hill; New York, 1953).Google Scholar
(3)Jones, D. S., and Whitham, G. B., Proc. Cambridge Philos. Soc. 53 (1957), 691.CrossRefGoogle Scholar
(4)Kodis, R. D., Proc. Cambridge Philos. Soc. 54 (1958), 612.CrossRefGoogle Scholar
(5)Levine, H., and Schwinger, J., Phys. Rev. 74 (1948), 958.CrossRefGoogle Scholar
(6)Lowan, A. N., Morse, P. M., Feshbach, H., and Lax, M., Scattering and radiation from circular cylinders and spheres (U.S. Navy Department, Office of Naval Research and Inventions; 1946).Google Scholar