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)/(2)sqrt2`

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)/(4mu))=(f)/(2sqrt2)`