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 .

Options

A. `230 Hz , 290 Hz`
B. `250 Hz , 300 Hz`
C. `264 Hz , 256 Hz`
D. `150 Hz , 300 Hz`

Answer

C

Explanation

Let `c` be the speed of sound and `f_(1) , f_(2)` be the frequency of tuning forks.
`f_(1) = ( c )/(4 l_(1)) = ( c )/( 4 xx 32) = ( c )/( 128)`
`f_(2) = ( c )/( 2 l_(2)) = ( c )/( 2 xx 66 ) = ( c )/( 132)`
Now `| f_(1) - f_(2)| = 8`
As `f_(1) gt f_(2)` we have `| f_(1) - f_(2)| = 8`
`( c )/(128) - ( c )/( 132) = 8`
`c = (128 xx 132 xx 8)/(4) = 33792 cm//s`
`f_(1) = ( c )/( 128) = 264 Hz`
`f_(2) = ( c )/( 132) = 256 Hz`