The modified phonon dispersion is of importance for understanding the origin of the reduced heat conductivity in nanowires. We have measured the phonon dispersion for 50 nm diameter InSb (111) nanowires using time-resolved X-ray diffraction. By comparing the sound speed of the bulk (3880 m/s) and that of a classical thin rod (3600 m/s) to our measurement (2880 m/s), we conclude that the origin of the reduced sound speed and thereby to the reduced heat conductivity is that the C44 elastic constant is reduced by 35% compared to the bulk material.