Spherical wave expansion coefficients for radiation from a planar velocity source.

Area of Science:

• Acoustics
• Wave Propagation
• Numerical Methods

Background:

• Spherical wave function expansions are crucial for analyzing sound fields.
• Calculating these coefficients from planar sources can be complex, especially in the near field.

Purpose of the Study:

• To present a general theory for obtaining spherical wave function expansion coefficients for sound beams from planar velocity sources.
• To simplify calculations by neglecting evanescent wave components and utilizing only the normal velocity condition.

Main Methods:

• Developed a general theory for spherical wave function expansion coefficients.
• Neglected evanescent wave components for an approximate near-field solution.
• Applied the theory to axisymmetric sources with simplifications.
• Compared results with direct numerical evaluation of the Rayleigh integral for circular and rectangular piston sources.

Main Results:

• The proposed method accurately obtains coefficients using only the normal velocity condition in the source plane, albeit as an approximation in the near field.
• Simplifications were successfully derived for axisymmetric sources.
• Validation against the Rayleigh integral showed good agreement for piston sources.

Conclusions:

• The presented theory provides an efficient method for calculating spherical wave function expansion coefficients.
• The approach is applicable to various planar velocity sources and simplifies acoustic analysis.
• Potential applications include acoustic scattering, radiation force calculations, and spherical acoustical holography.