Starting from the general expresson of frequency given by the dynamical theory of crystal lattices, we have derived three different expressions of the characteristic frequency for three kinds of solids, and re-obtained rS,rD-M and rf. We pointed out that rS,rD-M and rf. belong to three different models of solids. Finally, the general expressions of the characteristic frequency ω and Grüneisen coefficient γ for solids were found.