The theory of low-frequency wave physics revisited

The Stevenson approach to low-frequency time-harmonic wave scattering, that expanded the electric and magnetic fields in power series of k, essentially the inverse wavelength, is scrutinized. Stevenson's power series approach perforce implies a variable frequency ω, i.e., a variable wave-number k, an assumption challenged here. Presently the three major linear wave physics models: acoustics, electromagnetics, and elastodynamics, are put on an equal footing by introducing the self-consistent system concept. Accordingly any low-frequency series expansion starts with the pertinent Helmholtz equation. Far-field surface-integrals are derived for each case. To verify our approach, an example of low-frequency electromagnetic scattering by a long cylinder is elaborated, the results are compared to, and agree with the exact Hankel-Fourier series solution.