Acoustic scattering by inhomogeneous spheres

Area of Science:

• Acoustics
• Wave Propagation
• Materials Science

Background:

• Acoustic scattering analysis is crucial for understanding wave interactions with materials.
• Modeling inhomogeneous materials presents significant analytical challenges.
• Spherically symmetric material variations offer a tractable framework for acoustic studies.

Purpose of the Study:

• To derive explicit, separated solutions for acoustic scattering problems.
• To investigate scattering phenomena in media with spherically symmetric density and sound speed variations.
• To analyze specific cases involving inhomogeneous spheres and coatings.

Main Methods:

• Employing analytical methods to solve acoustic scattering equations.
• Deriving solutions for specific functional forms of density (rho) and sound speed (c).
• Utilizing Coulomb wave functions and Whittaker functions for the radial solutions.

Main Results:

• Explicit separated solutions were obtained for two distinct cases of spherically symmetric material parameters.
• The radial solutions were expressed in terms of well-established special functions.
• The study details scattering by an inhomogeneous sphere in a homogeneous fluid and by a homogeneous sphere with an inhomogeneous coating.

Conclusions:

• The derived solutions provide a mathematical framework for analyzing acoustic scattering in complex media.
• The use of special functions simplifies the analysis of these scattering problems.
• These results are applicable to scenarios involving layered or gradient materials.