Question

What factors decide the frequency of vibration of a plucked string

Answer 1

If the string is plucked hard, the amplitude will be higher means frequency will be low and the sound will be loud.
If the string is plucked correctly, the amplitude and frequency of the vibrating of the string will be good and the sound will  be melodious.

Answer 2

The four properties of the string that affect its frequency are length, diameter, tension, and density. These properties are described below: When the length of a string is changed, it will vibrate with a different frequency. Shorter strings have higher frequency and therefore higher pitch.