  We present direct observations of acoustic waves in warm dense matter. We
analyze wave-number- and energy-resolved x-ray spectra taken from warm dense
methane created by laser heating a cryogenic liquid jet. X-ray diffraction and
inelastic free-electron scattering yield sample conditions of 0.3$\pm$0.1 eV
and 0.8$\pm$0.1 g/cm$^3$, corresponding to a pressure of $\sim$13 GPa.
Inelastic x-ray scattering was used to observe the collective oscillations of
the ions. With a highly improved energy resolution of $\sim$50 meV, we could
clearly distinguish the Brillouin peaks from the quasielastic Rayleigh feature.
Data at different wave numbers were utilized to derive a sound speed of
5.9$\pm$0.5 km/s, marking a high-temperature data point for methane and
demonstrating consistency with Birch's law in this parameter regime.
