The frequency of vibration of a string depends on, (i) tension in the string (ii) mass per unit length of string, (iii) vibrating length of the string. Establish dimension the relation for frequency.

Explanation

`n prop I^(a) T^(b)m^(c), [I] = [M^(0)L^(1)T^(0)]`
`[T] = [M^(1)L^(1)T^(-2)]` (force)
`[M] = [M^(1) L^(-1) T^(0)]`
`[M^(0)L^(0)T^(-1)] = [M^(0)L^(1)T^(0)]^(a) [M^(1)L^(1)T^(-2)]^(b) [M^(0)L^(-1)T^(0)]^(c)`
b + c = 0
a + b - c = 0
-2b = -1 `rArr b = 1/2`
c `= -1/2 a = 1`
`n prop 1/l sqrt(T/m)`