The Spherical Wave Functions

2014 ◽  
pp. 11-26
Author(s):  
Sean F. Wu
Keyword(s):  
Spherical Wave ◽  
Wave Functions

Reconstruction of Acoustic Radiation of a Vibrating Structure Located in a Half-Space Bounded by a Passive Surface with Finite Acoustic Impedance

2020 ◽  
Vol 28 (04) ◽  
pp. 2050019
Author(s):  
Daren Zhou ◽  
Huancai Lu ◽  
D. Michael McFarland ◽  
Yongxiong Xiao
Keyword(s):  
Half Space ◽  
Acoustic Impedance ◽  
Free Space ◽  
Plane Surface ◽  
Spherical Wave ◽  
Boundary Surface ◽  
Sound Field ◽  
Wave Functions ◽  
Reconstruction Method ◽  
Direct Radiation

Vibrating structures are often mounted on or located near a passive plane surface with finite acoustic impedance, and hence the acoustic pressures measured in a half-space bounded by the surface consist of both the direct radiation from the structure and the reflection from the boundary surface. In order to visualize the direct radiation from the source into free space, a reconstruction method based on expansion in half-space spherical wave functions is proposed. First, the series of half-space spherical wave functions is derived based on the analytical solution of the sound field due to a multipole source located near an impedance plane. Then the sound field in the half-space is approximated by the superposition of a finite number of half-space expansion terms. The expansion coefficients are determined by solving an overdetermined linear system of equations obtained by matching this assumed solution to the total acoustic pressures in the half-space. The free-space radiation can finally be reconstructed via multiplying the free-space spherical wave functions by the corresponding coefficients. Numerical simulation examples of a vibrating sphere and a vibrating baffled plate are demonstrated. The effects of specific acoustic impedance of the boundary and the locations of the measurement points on the accuracy of reconstruction are examined.

scholarly journals Decomposition of scattered electromagnetic fields into vector spherical wave functions on surfaces with general shapes

2019 ◽  
Vol 99 (4) ◽  
Author(s):  
X. Garcia Santiago ◽  
M. Hammerschmidt ◽  
S. Burger ◽  
C. Rockstuhl ◽  
I. Fernandez-Corbaton ◽  
...  
Keyword(s):  
Electromagnetic Fields ◽  
Spherical Wave ◽  
Wave Functions

New series expansion representations for spherical wave functions

2000 ◽  
Vol 24 (2) ◽  
pp. 131-133 ◽  
Author(s):  
T. A. Laitinen ◽  
R. Sharma
Keyword(s):  
Series Expansion ◽  
Spherical Wave ◽  
Wave Functions

The Scattering Waves by Two Spheres in Solid

2013 ◽  
Vol 423-426 ◽  
pp. 1640-1643
Author(s):  
Yan Ru Zhang ◽  
Pei Jun Wei
Keyword(s):  
Wave Function ◽  
Cross Section ◽  
Spherical Wave ◽  
Addition Theorem ◽  
Wave Functions ◽  
Interface Condition ◽  
Elastic Sphere ◽  
Numerical Examples ◽  
Transmitted Waves ◽  
Expansion Coefficients

The scattering waves by two elastic spheres in solid are studied. The incident wave, the scattering waves in the host and the transmitted waves in the elastic spheres are all expanded in the series form of spherical wave functions. The total waves are obtained by addition of all scattered waves from individual elastic sphere. The addition theorem of spherical wave function is used to perform the coordinates transform for the scattering waves from different spheres. The expansion coefficients of scattering waves are determined by the interface condition between the elastic spheres and the solid host. The scattering cross section is computed as numerical examples.

Eigenvalues of a class of spherical wave functions

1973 ◽  
Vol 21 (1) ◽  
pp. 8-14 ◽  
Author(s):  
M. Narasimhan
Keyword(s):  
Spherical Wave ◽  
Wave Functions

scholarly journals SCALAR WAVES IN A WORMHOLE TOPOLOGY

2006 ◽  
Vol 15 (05) ◽  
pp. 669-693 ◽  
Author(s):  
NECMI BUĞDAYCI
Keyword(s):  
Wave Equation ◽  
Multiple Scattering ◽  
Infinite Series ◽  
Spherical Wave ◽  
Wave Functions ◽  
Scattering Method ◽  
Explicit Solutions ◽  
Scalar Wave ◽  
Scalar Wave Equation ◽  
Multiple Scattering Method

Global monochromatic solutions of the scalar wave equation are obtained in flat wormholes of dimensions (2+1) and (3+1). The solutions are in the form of infinite series involving cylindrical and spherical wave functions, and they are elucidated by the multiple scattering method. Explicit solutions for some limiting cases are illustrated as well. The results presented in this work constitute instances of solutions of the scalar wave equation in a space–time admitting closed time-like curves.

On: “DIFFRACTION OF ELECTROMAGNETIC WAVES BY AN INHOMOGENEOUS SPHERE” BY. J. G. NEGI (GEOPHYSICS, AUGUST 1962, PP. 480–492)

Geophysics ◽  
1963 ◽  
Vol 28 (4) ◽  
pp. 665-665
Author(s):  
Ari Ben‐Menahem ◽  
Armando Cisternas
Keyword(s):  
Electromagnetic Waves ◽  
Spherical Wave ◽  
Wave Functions ◽  
Inhomogeneous Sphere

In the section of the paper by Dr. Negi dealing with “The Influence of the Air‐Earth Boundary,” the author is using results given in a paper by B. P. Dyakonov (1959). Formula (28) in Dyakonov’s paper is incorrect because the spherical wave functions should be given differently.

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