  Taking the horizon surface of the black hole as a compact membrane and
solving the oscillation equation of this membrane by Klein-Gordon equation, we
derive the frequencies of oscillation modes of the horizon surface, which are
proportional to the radiation temperature of the black hole. However, the
frequencies of oscillation modes are not equidistant. Using the distribution of
obtained frequencies of oscillation mode we compute the statistic entropy of
the black hole and obtain that the statistic entropy of the black hole is
proportional to the area of the horizon. Therefore, it is proven that the
quantum statistic entropy of the black hole is consistent with
Bekenstein-Hawking entropy.
