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. First harmonic
B. 2f
C. `(f)/(2sqrt(2))`
D. `(f)/(2)sqrt(2)`

Answer

C

Explanation

As we have
`f = (1)/(2l) sqrt((T)/(mu))`
Ifradius is doubled and length is doubled, mass per unit length will become four times. Hence
`f = (1)/(2 xx 2l) sqrt((2T)/(4mu)) = (f)/(2sqrt(2))`