The coexistence of the transverse and fast sounds of liquid metals in the terahertz range near the melting point is explained. These sound modes are phonon polaritons arisen from the interaction between the transverse collective ionic oscillations, known as phonons, and the electromagnetic wave radiated by the ions in vibration at high enough frequencies, for instance, in liquid Zn, Cu, and Fe. Applying the phonon-polariton dispersion relations, several critical dynamic parameters of these liquid metals such as the structural relaxation times, speeds of the fast and transverse sound modes, dielectric constant at THz frequency are extracted, allowing to further understand dynamic behaviors of liquid metals at the atomic level. Phonon-polariton theory can be used for the study of the dynamics in the terahertz frequency range of similar liquid metals.