With the dispersion relation derived from the gyrokinetic equation with the plasma equilibrium toroidal rotation, the frequencies and damping rates of the geodesic acoustic modes, low frequency modes and sound wave branch are investigated, respectively. The results show that the frequency of the geodesic acoustic mode could increase with the toroidal rotation Mach number, while the collisionless damping rate will decrease with the toroidal rotation Mach number rapidly. In addition, the frequencies and damping rates of the low frequency modes and sound wave branches will decrease with the toroi...