  Temperature and magnetic field studies of the elastic constants of the
chromium spinel CdCr_2O_4 show pronounced anomalies related to strong
spin-phonon coupling in this frustrated antiferromagnet. A detailed comparison
of the longitudinal acoustic mode propagating along the [111] direction with
theory based on an exchange-striction mechanism leads to an estimate of the
strength of the magneto-elastic interaction. The derived spin-phonon coupling
constant is in good agreement with previous determinations based on infrared
absorption. Further insight is gained from intermediate and high magnetic field
experiments in the field regime of the magnetization plateau. The role of the
antisymmetric Dzyaloshinskii-Moriya interaction discussed and we compare the
spin-phonon coupling in CdCr_2O_4 in both the ordered and disordered states.
