Sound velocities of PbTe have been determined to 14 GPa using an ultrasonic interferometric method, which allowed for a detailed investigation of the characteristic variations of P and S wave velocities across the phase transitions from Fm3¯m (B1) to the orthorhombic Pbnm to Pm3¯m (B2). Elastic bulk and shear moduli and their pressure derivatives have been determined by fitting the measured velocities using a finite-strain approach. Based on the measured velocities and Debye theory, an estimate is made of the acoustic phonon contribution to the thermal conductivity, considering inter-phonon interactions only. By combining this result with previous determinations of the thermal conductivity due to electrons, the combination was found to have a significantly lower value than the previously determined total thermal conductivity. This is interpreted as evidence for coupling between the low-lying transverse optic (TO) and longitudinal acoustic (LA) modes, allowing the transfer of thermal energy from the acoustic to the optic modes. Possible explanations are discussed in the paper.