Brillouin scattering from transverse-acoustic modes of ${\mathrm{SrTiO}}_3$ is observed, while the frequencies of the soft polar modes are remeasured with hyper-Raman scattering. It is shown that an anomalous decrease of sound velocities at low temperatures results from the coupling of the strain with the gradient of the electrical polarization fluctuations. The corresponding anomaly in the acoustic width indicates an inhomogeneous broadening of the soft polar mode.

• Received 12 February 1998

DOI:https://doi.org/10.1103/PhysRevB.57.R13989