Since eq.(30) is quadratic in the solutions may be written in the form:
and
where, as will be seen shortly, and correspond to inertia-gravity wave and acoustic wave frequencies respectively.
For terrestrial values of , and , some simplification of eqs.(31) and (32) is possible. Consider the ratio of to i.e.
Taking , and , the term on the right of the inequality above is and so can be safely neglected in the dispersion equations for gravity and acoustic waves giving:
and
A further simplification arises because of the smallness of the term: