The principle and method of the magneto-optical modulation measuring the Faraday effect in a sine magnetic field have been proposed. A theoretical analysis has been performed on the magnetic field-frequency dependence of both the Faraday effect and the degree of the magneto-optical modulation in ferrimagnetic medium.It has been shown that θ',the real part of the Faraday rotation θ,in an alternating magnetic field is smaller than that in a static field, while the imaginary part θ″ is larger than that in a static field. The theory corresponds with the experimental results. The conclusion has been drawn that it is imposible to realize complete on-off switch by a modulator utilizing magneto-optical materials with magnetic circular dichroism.