Synopsis
Explore the exact theory behind diffraction by a circular disk and see how it compares with common approximations.
This book develops a detailed, first‑principles view of how waves scatter from a disk, using the oblate spheroidal wave functions that naturally fit this geometry. It contrasts acoustic results with electromagnetic cases and shows why certain vector solutions are easier to handle in some problems than in others.
Starting from fundamental wave equations and Green’s function techniques, the text explains how the distant field and scattering cross sections are obtained, and how the parameter ka (the ratio of disk diameter to wavelength) governs the behavior of the solution. The discussion covers exact results for sound by a perfectly rigid disk and outlines the challenges of extending these methods to electromagnetic waves, where vector fields add complexity.
- How exact solutions are built from oblate spheroidal wave functions for normal incidence.
- The meaning of ka and how it shapes diffraction patterns and resonances.
- Where Kirchhoff’s theory aligns with or diverges from exact results in acoustics.
- Qualitative behavior near the disk edge, including singularities in velocity components.
Ideal for readers of wave physics, acoustics, and mathematical methods in diffraction, this edition clarifies when approximate theories are useful and when exact results are needed.
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