The frequency `f` of vibration of a string between two fixed ends is proportional to `L^(a) T^(b) mu^(c )`, where `L` is the length of string, `T` is tension in the string and `mu is the linear mass density (or mass per unit length) of string. Find the value of a,b and c.

Explanation

`f prop L^(a) T^(b) mu^(C )`
`T^(-1) prop [L]^(a) [MLT^(-2)]^(b) [ML^(-1)]^(C )`
`m^(0) L^(0) T^(-1) prop^(b + c) L^(a + b + c) T^(-2b)`
Comparing the power of `M, L` and `T`
`b + c = 0`
`a + b - c = 0`
`-2b = -1`
`b = (1)/(2), c = - (1)/(2), a = - 1`