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 2 T and radius 2 r 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 becomes four times. Hence
`f'=1/(2xx2l) sqrt((2T)/(4mu)) =f/(2sqrt(2))`