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 become four times. Hence `f'=1/(2xx2l)sqrt((2T)/(4 mu))=1/(2sqrt(2))`