  We calculate the collective excitations of a dipolar Bose-Einstein condensate
in the regime where it self-binds into droplets stabilized by quantum
fluctuations. We show that the filament-shaped droplets act as a
quasi-one-dimensional waveguide along which low angular momentum phonons
propagate. The evaporation (unbinding) threshold occurring as the atom number
$N$ is reduced to the critical value $N_c$ is associated with a monopole-like
excitation going soft as $\epsilon_0\sim(N-N_c)^{1/4}$. Considering the system
in the presence of a trapping potential, we quantify the crossover from a
trap-bound condensate to a self-bound droplet.
