The basic vibrational properties of a hexagonal lattice (graphite-type) were found from the dynamic matrix which has all the system symetries, within the harmonic approximation and taking only first-neighborg interactions, only two independent parameters were determined: one of them describes the central forces effects; other one the non-central forces. The dispersion relations obtained analytically, are presented in three-dimensional plots for the first Brillouin-zone and along lines of hight symmetry. From a pedagogical point of view, we have depeloped a realistic example (non-trivial) for the phonon study in an introductory course.