Abstract: For the string vibrating problem under the condition that one end is fixed and the other end with sinusoidal incentive，it is solved by the separation of variables under incentive of resonant frequency and non-resonant frequency. Through the study of two different forms of solutions，it is found that the solution under the resonant frequency incentive can be obtained by getting the limit of the solution under non-resonant frequency incentive. Finally，the analysis shows that the solution under resonant frequency incentive is the solution of standing wave state without damping.

Key words: string vibrating equation, resonant frequency, separation of variables, standing wave