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

The fundamental frequency of wire vibrating under tension T is given by
`f_1=1/2sqrt(T/mu)`
Here, `mu` = mass of string per unit length.
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)`
`thereforef_1=15/16`
therefore`f_1=16/15xxf_1`
`Rightarrow therefore f_2=16/15xx6+x`
Taking two cases of 4 and equating both, we have `(x+6)=16/15(x-6)`
`therefore 15x+90=16x-96`
`therefore x=186Hz`