  Using an effective field theory we study the low-lying bosonic excitations
and their couplings to phonons at ultrasonic frequencies in superfluid $^3$He-B
under strong confinement. We show that confinement induces a rich spectrum of
low-lying bosons, including surface-bound bosonic states, as well as fine
structure of long-lived massive bosons. Under sufficiently strong confinement
we find a dynamical instability of the $^3$He-B film: the frequency of the
surface-bound boson softens at finite wavevector, then develops a pole in the
upper half of the complex frequency plane, signalling a dynamical instability
of the translationally invariant superfluid vacuum towards pair-density-wave
"crystallization". We discuss the signatures and observability of the low-lying
bosonic spectrum based on analysis of the ultrasound attenuation from resonant
excitation of the bosonic modes. We also note that surface-bound bosonic modes
are not unique to $^3$He-B, but are expected to be common to unconventional
superconductors with a multi-component order parameter.
