Acoustic, Gravity, & Acoustic-Gravity Waves

Assume a plasma with no magnetic field (B=0) at rest with constant density, ρ₀, undergoes a small perturbation (subscripts 1) resulting in a plasma flow such that,

ρ = ρ₀ + ρ₁,
v = v₁.

Differentiating Eqn. 23 with respect to time, substituting linearised forms of Eqn. 17 and Eqn. 21, and assuming an isothermal, gravitationally stratified atmosphere as before leads to a generalised wave equation,

Once again plane wave solutions for v₁ exist of of the form,

where propagation is along the wavevector k (). Hence, as before, and in Eqn. 39, which becomes,

which forms the basis for discussing acoustic and gravity waves.