A string of length l' fixed at both ends vibrates in resonance with a tuning fork of frequency 'f' at two successive values of tension `T_(1)` and `T_(2)` inthe string. Findthe specificmass (mass per unit length) ofthe string:

Options

A. `(T_(1)T_(1))/(f^(2)l^(2)(sqrt(T_(1)) - sqrt(T_(2)))^(2))`
B. `(2T_(1)T_(1))/(f^(2)l^(2)(sqrt(T_(1)) - sqrt(T_(2)))^(2))`
C. `(T_(1)T_(1))/(2f^(2)l^(2)(sqrt(T_(1)) - sqrt(T_(2)))^(2))`
D. None of these

Answer

D

Explanation

We use
`f = (n+1)/(2l) sqrt((T_(2))/(mu))`
`f = (n+1)/(2l) sqrt((T_(2))/(mu))`
from equation (1) and (2) eliminate 'n' to get `mu`.
`mu = (T_(1)T_(2))/(4f^(2)l^(2)(sqrt(T_(1)) - sqrt(T_(2)))^(2))`