  We calculate the electronic polarizability in the superconducting state near
extremum vectors ${\vec Q}_0$ of the Fermi surface. A pole appears in the
polarizability at frequencies $\omega$ near the superconducting gap $2\Delta$
which leads to a sharp peak at $\omega$ just below $2 \Delta$ in the lattice
vibrations near ${\vec Q}_0$. A second order transition to a charge density
wave state below the superconducting transition is shown to be unlikely. The
results are compared with the recent inelastic neutron scattering measurements
in compounds, $ANi_2B_2C$, $A=Y$ or $Lu$.
