We present the results of a computer simulation study of the longitudinal dispersion curves of a model core-softened liquid and the SPC/E water model. We have shown that the excitation frequencies decreased with temperature along isochors in both systems. This behavior is contrary to the normal liquids. We have introduced new water anomaly: anomalous dependence of excitation frequencies on temperature. (C) 2019 Elsevier B.V. All rights reserved.