A somometer wire produces 2 beats per second with a tuning fork, when the length of the wire is either 102cm or 104 cm . The frequency of the tuning fork is

Explanation

Let ` n_(1) and n_(2)` be the frequencies of the sonomter wire for lengths `L_(1) and L_(2)`. Let N be the frequency of the turing fork.
` n_(1) L_(1) = n_(2)L_(2) " " n_(2) = n_(1) L_(1)/L_(2)`
Here, ` L_(2) gt L_(1) " " n_(2) lt n_(1) " " n_(1) gt N gt n_(2)`
`n_(1) -N = 5 and N-n_(2) = 5 " " therefore n_(1) -n_(2) =10`
`n_(1) - n_(2) L_(1)/L_(2) = 10 " " therefore n_(1) (1-L_(1)/L_(2)) = 10`
` n_(1) ((L_(2)-L_(1))/L_(2))= 10`
` n_(1) = (L_(2)/(L_(2)-L_(1)) xx 10 = (40.5/ (40.5 - 39.5))xx 10`
`= 40.5 xx 10 = 405 Hz`
` N= n_(1) -5 = 405 -5 = 400 Hz`