Gain dynamics and refractive index changes in fiber amplifiers are important in many areas. For example, the knowledge of the frequency responses for seed and pump power modulation are required to actively stabilize low noise fiber amplifiers. Slow and fast light via coherent population oscillations rely on the change of group index to delay or advance pulses, and refractive index changes in fiber amplifiers are a possible explanation for mode fluctuations in high power fiber amplifiers. Here, we analyze the frequency dependent influence of seed and pump power modulation on the fiber amplifier output power and the refractive index. We explain the observed power and refractive index modulation with an analytic model originally developed for telecom amplifiers and discuss a further simplification of the model.