Two forks A and B when sounded together produce
four beats `s^(-1)`. The fork A is in unison with 30 cm
length of a sonometer wire and B is in unison with 25
cm length of the same wire at the same tension. The
frequencies of the forks are

Explanation

As in case of vibrations of string under specific tension, we know that frequency `n infty (1//L)` or `n = (k//L)`. As forks A and B are in unison {equalfrequencies) with 30 cm and 25 cm length ofa given sonometer wire respectively. If `n_(A)` and `n_(B)` be the frequencies of the two turning forks, we have,
`n_(A) = (K)/(30)` and `n_(B) = (K)/(25)`
`(n_(A))/(n_(B)) = (25)/(30)`
Further as the forks A and B produce 4 beats when sounded together
`n_(A) n_(B) = 4`
Butfrom equation-(6.248) it isclear that `n_(A) lt n_(B)`
Thus we have `n_(B) - n_(A) = 4`
Solving equation-(6.248) and (6.249) for `n_(A)` and`n_(B)` we get
`n_(A) = 20Hz` and `n_(B) = 24 Hz`