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LOW-FREQUENCY ACOUSTIC SCATTERING OF A PLANE WAVE FROM A SOFT AND HARD TORUS.
- Source :
-
Journal of Computational Acoustics . Jun2007, Vol. 15 Issue 2, p181-197. 17p. - Publication Year :
- 2007
-
Abstract
- A plane acoustic wave is scattered by either a soft or a hard small torus. The incident wave has a wavelength which is much larger than the characteristic dimension of the scatterer and thus the low-frequency approximation method is applicable to the scattering problem. It is shown that there exists exactly one toroidal coordinate system that fits the given geometry. The R-separation of variables is utilized to obtain the series expansion of the fields in terms of toroidal harmonics (half-integer Legendre functions of first and second kind). The scattering problem for the soft torus is solved analytically for the near field, governing the leading two low-frequency coefficients, as well as for the far field, where both the amplitude and the cross-section are evaluated. The scattering problem for the hard torus appears to be much more complicated in calculations. The Neumann boundary condition on the surface of the torus leads to a three-term recurrence relation for the series coefficients corresponding to the scattered fields. Thus, the potential boundary-value problem for the leading low-frequency approximations is reduced to infinite systems of linear algebraic equations with three-diagonal matrices. An analytical technique for solving systems of diagonal form is developed. [ABSTRACT FROM AUTHOR]
- Subjects :
- *SCATTERING (Physics)
*SOUND
*WAVES (Physics)
*TOROIDAL harmonics
*EQUATIONS
Subjects
Details
- Language :
- English
- ISSN :
- 0218396X
- Volume :
- 15
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Computational Acoustics
- Publication Type :
- Academic Journal
- Accession number :
- 27176373
- Full Text :
- https://doi.org/10.1142/S0218396X07003299