  We present an experimental and theoretical study of the high-energy
excitation spectra of a dipolar supersolid. Using Bragg spectroscopy, we study
the scattering response of the system to a high-energy probe, enabling
measurements of the dynamic structure factor. We experimentally observe a
continuous reduction of the response when tuning the contact interaction from
an ordinary Bose-Einstein condensate to a supersolid state. Yet the observed
reduction is faster than the one theoretically predicted by the
Bogoliubov-de-Gennes theory. Based on an intuitive semi-analytic model and
real-time simulations, we primarily attribute such a discrepancy to the
out-of-equilibrium phase dynamics, which although not affecting the system
global coherence, reduces its response.
