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/(2sqrt2)`
D. `f/2sqrt2`

Explanation

`f=1/(2l)sqrt(T/mu)`
If radius is doubled and length is doubled, mass per unit length will become four times. Hence
`f'=1/(2xx2l)=sqrt((2T)/(4mu))=f/(2sqrt2)`