How does the frequency of a vibrating string vary with its density and radius?

State the formula for frequency of a vibrating string.

In an experiment it is observed that the frequency of a vibrating string depends on length the tension and the mass per unit length . Find out a relation for the frequency from dimensional analysis.

The fundamental frequency of vibration of a stretched string is 200Hz . Find the frequency of the vibration if the tension increases four times and length is reduced to one fourth the original values

How we explain amplitude of vibration ?