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

Answer

C

Explanation

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