Question

The frequency of vibration (f) of a string may depend upon length (l) of the string, tension (T), and mass per unit length (m).Use method of dimension for establishing the formula for frequency.

Answer 1

The general procedure is
Take,\[f = l^x T^y m^z\]
where x,y,z are some constants.
Now write the dimensional formula for each of them.
f-T^-1
l-L
T- dimension of force
m- ML^-1
Now solve by equating the powers.