Waves in a Uniform Medium: Special Cases

We consider the special case of an infinite, uniform medium with B ₀ = B ₀ ê _z and J ₀ = 0. In that case we can expand an arbitrary displacement in plane wave solutions as where k is the wave vector and the addition of the complex conjugate is implied. When we substitute this into the ideal MHD wave equation, we find that ∇→i k and ∂ /∂t → iω, so that the problem is reduced to algebra.

I’m pickin’ up good vibrations.

The Beach Boys