Statistical information on the phonon frequency spectrum of materials can be obtained by neutron transmission techniques if they contain nuclei with low energy resonances, narrow enough to be Doppler-broadened. We have carried out measurements using this technique for the doped 2-1-4 system, La2.xBaxCuO4. Two samples with slightly different concentrations of barium, one superconducting, the other not, were examined. Pure Lanthanum Cuprate was also studied. Neutron cross section measurements have been made with high energy resolution and statistical precision on the 60m flight path of LANSCE, the pulsed spallation neutron source at Los Alamos National Laboratory. Measurements on all three materials were made over a range of temperatures from 15K to 300K, with small steps through the critical temperature region near 27K. No significant changes in the mean phonon energy of the lanthanum atoms were observed near the critical temperature of the super-conducting material. It appears however that the mean phonon energy of lanthanum in the superconductor is considerably higher than that in the non-superconductors.