The beat frequency characteristic of a He-Ne laser with an activity plate in its cavity is studied. The laser physics and crystal optics are used to solve the problem. One mode of laser splits into two eigenstates of crystal as it transmits in the plate. G is the ratio of them, so the time delay of the mode is between those of two eigenstates. The time delay of another mode is also between those of them. So that, the beat freauency is always less than what is determined by the phase difference of two eigenstates. It is related to the special factor G2. Theoretical result matches the experiment very well.