Discussion
Which relation must a wave satisfy to be a solution of the equations?
Answer: D
Substituting a wave solution into the linearised equations yields an algebraic relation between frequency and wavenumber that must hold for the solution to exist. That dispersion relation encodes the whole propagation behaviour of the wave type. Continuity, hydrostatic balance and the thermal wind relation are among the equations from which the dispersion relation is derived rather than substitutes for it. A limit that survives making every external component ideal is an intrinsic one, and worth knowing for that reason.
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