The frequency noise spectrum of a magnetic tunnel junction based spin torque oscillator is examined where multiple modes and mode-hopping events are observed. The frequency noise spectrum is found to consist of both white noise and 1/f frequency noise. We find a systematic and similar dependence of both white noise and 1/f frequency noise on bias current and the relative angle between the reference and free layers, which changes the effective damping and hence the mode-hopping behavior in this system. The frequency at which the 1/f frequency noise changes to white noise increases as the free layer is aligned away from the anti-parallel orientation w.r.t the reference layer. These results indicate that the origin of 1/f frequency noise is related to mode-hopping, which produces both white noise as well as 1/f frequency noise similar to the case of ring lasers.