Question

Which factor decided the frequency of vibration of a plucked string

Answer 1

If the string is plucked hard the amplitude will be greater than its frequency in the given time. But when the string is perfectly plucked by length and with perfection ,the sound produced is melodious because now,
amplitude = frequency.

Thus the vibration of a plucked string depends on its length, tension and frequency.

Hope it helps !!!

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.