Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 

 

The reflection coefficient of a surface of Rayleigh distributed impedance


Author: H. S. Heaps
Journal: Quart. Appl. Math. 15 (1957), 291-297
MSC: Primary 60.0X
DOI: https://doi.org/10.1090/qam/90162
MathSciNet review: 90162
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Formulas are obtained for the probability distribution $ p\left( k \right)$ of the amplitude $ k$ of $ {\left( {z - {c_2}} \right)^2}{\left( {z + {c_1}} \right)^{ - 2}}$ in which $ {c_1}$ and $ {c_2}$ are real constants. $ z$ is a complex number of the form $ c + {z_1}$ where $ c$ is a complex constant and $ {z_1}$ is a complex variable of Gaussian distribution of amplitude and uniform distribution of phase (see Fig. 1).


References [Enhancements On Off] (What's this?)

  • [1] P. M. Morse, Some aspects of the theory of room acoustics, J. Acoust. Soc. Amer. 11, 56-66 (1939)
  • [2] P. M. Morse, Vibration and sound, 2nd. ed., McGraw-Hill Book Co., New York, 1948
  • [3] R. A. Scott, The propagation of sound between walls of porous material, Proc. Phys. Soc. 58, 358-368 (1946)
  • [4] G. D. Monteath, Application of the compensation theorem to certain radiation and propagation problems, Proc. I.E.E., Part 4, 98, 23-30 (1951)
  • [5] S. A. Schelkunoff, Electromagnetic waves, D. van Nostrand Co., New York, 1943
  • [6] H. S. Heaps, Reflection of a plane acoustic wave from a surface of non-uniform, impedance, J. Acoust. Soc. Amer. 28, 666-671 (1956)
  • [7] G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, England; The Macmillan Company, New York, 1944. MR 0010746
  • [8] Eugene Jahnke and Fritz Emde, Tables of Functions with Formulae and Curves, Dover Publications, New York, N. Y., 1945. 4th ed. MR 0015900
  • [9] K. Pearson, Tables of the incomplete $ \Gamma $-function, Re-issue, Cambridge University Press, London, 1946
  • [10] Bateman Manuscript Project, Higher transcendental functions, vol. 2, McGraw-Hill Book Co., New York, 1953

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 60.0X

Retrieve articles in all journals with MSC: 60.0X


Additional Information

DOI: https://doi.org/10.1090/qam/90162
Article copyright: © Copyright 1957 American Mathematical Society


Brown University The Quarterly of Applied Mathematics
is distributed by the American Mathematical Society
for Brown University
Online ISSN 1552-4485; Print ISSN 0033-569X
© 2017 Brown University
Comments: qam-query@ams.org
AMS Website