Attenuated Total Reflectance was used to measure phonon vibration frequencies over the range 425-800 cm(-1) of SrTiO3 thin films deposited either directly on LaAlO3, or on YBCO-coated LaAlO3 single crystal substrates. In the s-polarized spectra, the transverse optic Ti-O stretching vibration shifted to lower frequencies as the film thickness increased, which was attributed to damping caused by the generation of lower frequency phonon modes. The transverse Ti-O stretching vibration was also observed in the p-polarized spectra, but was more heavily damped, which indicates the damping is more pronounced when the electric field has a component perpendicular to the film surface. Damping of the transverse modes was attributed to coupling of these modes to other phonon modes, and may be a source of the high losses at microwave frequencies.