A wire of length l having tension T and radius `r` vibrates with fundamental frequency `f`. Another wire of the same metal with length `2l` having tension `2T` and radius `2r` will vibrate with fundamental frequency :

Options

A. f
B. 2f
C. `f/(2sqrt(2))`
D. `f/2sqrt(2)`

Answer

C

Explanation

`f=1/(2l) sqrt(T/(mu))`
If radius is doubled and length is doubled, mass per unit length will becomes four times. Hence
`f'=1/(2xx2l) sqrt((2T)/(4mu)) =f/(2sqrt(2))`