  We study the spectrum of elementary excitations of a dipolar Bose gas in a
three-dimensional anisotropic trap across the superfluid-supersolid phase
transition. Theoretically, we show that, when entering the supersolid phase,
two distinct excitation branches appear, respectively associated with
dominantly crystal and superfluid excitations. These results confirm
infinite-system predictions, showing that finite-size effects play only a small
qualitative role, and connect the two branches to the simultaneous occurrence
of crystal and superfluid orders. Experimentally, we probe compressional
excitations in an Er quantum gas across the phase diagram. While in the
Bose-Einstein condensate regime the system exhibits an ordinary quadrupole
oscillation, in the supersolid regime we observe a striking two-frequency
response of the system, related to the two spontaneously broken symmetries.
