  The number of absorption and Raman optical modes for each Wyckoff orbit in
the high-temperature tetragonal (I4/mmm) parent lattice of the
Ruddlesden-Popper compounds Ca$_3$X$_2$O$_7$, with X=Mn or X=Ti is given. We
analyze the effect of sequential perturbations which lower the symmetry to Cmcm
and Cmc2$_1$ and finally include magnetic ordering. We determine the power law
behavior (within mean field theory) for the cross section for photon absorption
and Raman scattering of modes which appear as the symmetry is successively
lowered. In the Cmc2$_1$ phase we give a symmetry analysis to discuss the
magnon-phonon coupling which in other systems gives rise to "electromagnons."
From our results we suggest several experiments to clarify the phase diagram
and other properties of these systems.
