The dispersion of longitudinal acoustic phonons was measured by inelastic x
-ray scattering in the hexagonal closed-packed (hcp) structure of iron from
19 to 110 gigapascals. Phonon dispersion curves were recorded on polycryst
alline iron compressed in a diamond anvil cell, revealing an increase of th
e Longitudinal wave velocity (V-p) from 7000 to 8800 meters per second. We
show that hcp iron follows a Birch law for V-p, which is used to extrapolat
e velocities to inner core conditions. Extrapolated Longitudinal acoustic w
ave velocities compared with seismic data suggest an inner core that is 4 t
o 5% Lighter than hcp iron.