Wire having tension 225 N produces six beats per second when it is tuned with a fork. When tension changes to 256 N, it is tuned with the same fork, the number of beats remain unchanged. The frequency of the fork will be

Options

A. 186 Hz
B. 225 Hz
C. 256 Hz
D. 280 Hz

Answer

a

Explanation

Acceording to question, the fundamental frequency of
wire vibrating under tension T is given by
`f_(1)=1/2 sqrt(T/mu)`
Here, `mu =` mass of string per unit lenngth.
Let the frequency of tunning fork be x which beat, 6 beats
per second.
Let `(x-f)pm 6`
`therefore f_(1) = 1/(2L)sqrt(225/mu)and f_(2)=1/(2L)sqrt(256/mu)`
`therefore f_(1)/(f_(2))=15/16`
` therefore f_(2)=16/15xxf_(1)rArr f_(2)=16/15 (6+x)`
Taking two cases of `f_(1)` and equating both, we have
`(x+6) = 16/15(x-6)`
`therefore 15x +90 =16x-96`
`therefore x=186 Hz`