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Diffraction by a Half-Plane

Published online by Cambridge University Press:  20 January 2009

Ll. G. Chambers
Ll. G. Chambers
Affiliation:
Royal Military College of Science, Shrivenham, Wilts.
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The diffraction of a simple harmonic wave train by a straightedged semi-infinite screen was originally discussed by Sommerfeld in 1895. The analysis is of a recondite character, involving the use of multivalued functions and Riemann surfaces (1). An alternative formulation of the problem is as an inhomogeneous Wiener-Hop integral equation, the solution of which also involves considerable difficulties (2). It is the purpose of this note to show that following Friedlander (3) it is possible by the use of parabolic co-ordinates to solve the problem by elementary methods. The method can be applied either to the case of sound or that of electromagnetism, the results being formally identical.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 10 , Issue 2 , December 1954 , pp. 92 - 99
Copyright
Copyright © Edinburgh Mathematical Society 1954

References

REFERENCES

(1)See for example, Handbuch der Physik, Vol. XX,263–291, “Lichtals Wellenbewegung.”Google Scholar
(2)Copson, , 1946. “An integral equation method of solving plane diffraction problems,” Proc. Roy. Soc., A 186, 100–118.Google Scholar
(3)Friedlander, , 1946. “The diffraction of sound pulses. I. Diffraction by a semiinfinite plane,” Proc. Roy. Soc., A 186, 322–344.Google ScholarPubMed