Acoustic anomalies of relaxor ferroelectric Na1/2Bi1/2TiO3 single crystals were investigated over a wide temperature range from -196 degrees C to 900 degrees C by using Brillouin spectroscopy. The longitudinal sound velocity, the acoustic absorption coefficient and the elastic constant C-11 were determined for the acoustic phonon mode propagating in the [100] direction. Two acoustic anomalies, weaker ones at the cubic-tetragonal phase transition temperature of similar to 540 degrees C and more pronounced ones at temperatures near 315 degrees C near the dielectric maximum temperature, were investigated and discussed in relation with the relevant order parameters coupled to the acoustic waves. The relaxation dynamics in the cubic phase were studied based on the flattening of the mode frequency and the half width, which was observed for the first time, and a modified Arrhenius law.