We studied the nuclear resonant x-ray scattering of iron hydride (FeHx) up to 52 GPa. Coupled with hydrostatic x-ray diffraction data, the partial phonon density of states measured by nuclear resonant inelastic x-ray scattering provides information on sound velocities and the Fe contribution to thermodynamic parameters. In particular it constrains the aggregate shear velocity and shear modulus for comparison to seismic observations. We found that VS (km/sec) = 0.023*P (GPa) + 3.2. A loss of magnetism was observed with synchrotron M¿ssbauer spectroscopy at 22 GPa, lower than theoretically predicted but consistent with the observed anomalous velocity behavior. Results confirm that FeHx could be a major light element bearing phase for explaining the core density deficit relative to pure Fe. Formation of FeHx by reaction with water would be expected to leave a signature in the mantle.