A tuning fork `A` is in resonance with an air column ` 32 cm` long and closed at one end . When the length of this column is increased by `1 cm`,it is in resonance with another fork `B`. When `A and B` are sounded together , they produce `40 "beats in" 5 s`. Find their frequencies .

Explanation

`n_(A) = ( c )/( 4 xx 0.32) and n_(B) = ( c )/( 4 xx 0.33)`
Obviously ` n_(A) gt n_(B)`
`:. ( c )/( 4 xx 0.32) - ( c) /(4 xx 0.33) = 8 or c = 337.92 m//s`
`:. N_(A) = ( 337.92)/(4 xx 0.32) = 264 Hz`
and `n_(B) = 264 - 8 = 256 Hz`