  We present an experimental and theoretical study of the phonon mode in a
unitary Fermi gas. Using two-photon Bragg spectroscopy, we measure excitation
spectra at a momentum of approximately half the Fermi momentum, both above and
below the superfluid critical temperature $T_\mathrm{c}$. Below $T_\mathrm{c}$,
the dominant excitation is the Bogoliubov-Anderson (BA) phonon mode, driven by
gradients in the phase of the superfluid order parameter. The temperature
dependence of the BA phonon is consistent with a theoretical model based on the
quasiparticle random phase approximation in which the dominant damping
mechanism is via collisions with thermally excited quasiparticles. As the
temperature is increased above $T_\mathrm{c}$, the phonon evolves into a
strongly damped collisional mode, accompanied by an abrupt increase in spectral
width. Our study reveals strong similarities between sound propagation in the
unitary Fermi gas and liquid helium.
