A detailed analysis of the method of picosecond acoustic interferometry to study attenuation and velocity of longitudinal acoustic phonons in transparent materials in the Brillouin frequency range with picosecond laser pulses is presented. Experimental results for fused quartz from 90 to 300 K show good agreement with previous Brillouin scattering data. Measurements on a borosilicate glass (Corning 7059) and sapphire have also been made. This method makes these measurements possible under conditions where conventional approaches are not applicable.