  We study phonons in MgB2 using inelastic x-ray scattering (1.6 and 6 meV
resolution). Our measurements show excellent agreement with theory for the
dispersion and line-width: we clearly observe the softening and broadening of
the crucial E2g mode through the Kohn anomaly along GM. Low temperature
measurements (just above and below Tc) show negligible changes for the
momentum-transfers investigated, and no change in the E2g mode at A between
room temperature and 16K. We report the presence of a longitudinal mode along
GA near in energy to the E2g mode that is not predicted by theory.
