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
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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).
P. M. Morse, Some aspects of the theory of room acoustics, J. Acoust. Soc. Amer. 11, 56-66 (1939)
P. M. Morse, Vibration and sound, 2nd. ed., McGraw-Hill Book Co., New York, 1948
R. A. Scott, The propagation of sound between walls of porous material, Proc. Phys. Soc. 58, 358-368 (1946)
G. D. Monteath, Application of the compensation theorem to certain radiation and propagation problems, Proc. I.E.E., Part 4, 98, 23-30 (1951)
S. A. Schelkunoff, Electromagnetic waves, D. van Nostrand Co., New York, 1943
H. S. Heaps, Reflection of a plane acoustic wave from a surface of non-uniform, impedance, J. Acoust. Soc. Amer. 28, 666-671 (1956)
- G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, England; The Macmillan Company, New York, 1944. MR 0010746
- Eugene Jahnke and Fritz Emde, Tables of Functions with Formulae and Curves, Dover Publications, New York, N. Y., 1945. 4th ed. MR 0015900
K. Pearson, Tables of the incomplete $\Gamma$-function, Re-issue, Cambridge University Press, London, 1946
Bateman Manuscript Project, Higher transcendental functions, vol. 2, McGraw-Hill Book Co., New York, 1953
P. M. Morse, Some aspects of the theory of room acoustics, J. Acoust. Soc. Amer. 11, 56-66 (1939)
P. M. Morse, Vibration and sound, 2nd. ed., McGraw-Hill Book Co., New York, 1948
R. A. Scott, The propagation of sound between walls of porous material, Proc. Phys. Soc. 58, 358-368 (1946)
G. D. Monteath, Application of the compensation theorem to certain radiation and propagation problems, Proc. I.E.E., Part 4, 98, 23-30 (1951)
S. A. Schelkunoff, Electromagnetic waves, D. van Nostrand Co., New York, 1943
H. S. Heaps, Reflection of a plane acoustic wave from a surface of non-uniform, impedance, J. Acoust. Soc. Amer. 28, 666-671 (1956)
G. N. Watson, A treatise on the theory of Bessel functions, 2nd. ed., Cambridge University Press, London, 1944
E. Jahnke and F. Emde, Tables of functions, Dover Publications, New York, 1945
K. Pearson, Tables of the incomplete $\Gamma$-function, Re-issue, Cambridge University Press, London, 1946
Bateman Manuscript Project, Higher transcendental functions, vol. 2, McGraw-Hill Book Co., New York, 1953
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Article copyright:
© Copyright 1957
American Mathematical Society
