Two tuning forks `A and B` produce ` 4 beats//s` when sounded together . `A` resonates to `32.4 cm` of stretched wire and `B` is in resonance with `32 cm` of the same wire . Determine the frequencies of the two tuning forks .

Explanation

Let `f_(1) and f_(2)` be the frequencies of the tuning forks `A and B` respectively .
Since , the beat frequency between `A and B is 4`
`:. F_(1) - f_(2) = 4 or f_(2) - f_(1) = 4`
From, `n = (1)/ ( 2l) sqrt(T//mu)` , we have , `n prop 1//l`
`:. f_(1) prop (1)/(32.4) cm and f_(2) prop 1//32 cm`
`:. "Evidently" , f_(2) gt f_(1)`
`:. f_(2) - f_(1) = 4 s^(-1)` (i)
Also , `(f_(2))/(f_(1)) = ( 324)/( 320)` (ii)
Solving Eqs . (i) and (ii) , we get
`f_(1) = 320 Hz and f_(2) = 324 Hz`