We report a linear dependence of the phonon splitting Δω on the nondominant exchange coupling constant J(nd) in the antiferromagnetic transition-metal monoxides MnO, FeO, CoO, NiO, and in the frustrated antiferromagnetic oxide spinels CdCr(2)O(4), MgCr(2)O(4), and ZnCr(2)O(4). It directly confirms the theoretical prediction of an exchange-induced splitting of the zone-center optical phonon for the monoxides and explains the magnitude and the change of sign of the phonon splitting on changing the sign of the nondominant exchange also in the frustrated oxide spinels. The experimentally found linear relation [symbol:see text}Δω=βJ(nd)S(2) with slope β=3.7 describes the splitting for both systems and agrees with the observations in the antiferromagnets KCoF(3) and KNiF(3) with perovskite structure and negligible next-nearest neighbor coupling. The common behavior found for very different classes of cubic antiferromagnets suggests a universal dependence of the exchange-induced phonon splitting at the antiferromagnetic transition on the nondominant exchange coupling.