The conditions for string vibration to form a stable standing wave are: 1. Both ends of the string must be fixed and cannot move freely. 2. The string must be vibrated at a constant frequency, i.e. the frequency must be the resonant frequency. 3. The length of the string must be proportional to an integer multiple of the wavelength, which satisfies the condition of harmonics. Only when the above three conditions are met, a stable standing wave can be formed.