A closed air column `32 cm` long is in resonance with a tuning fork . Another open air column of length `66 cm` is in resonance with another tuning fork . If the two forks produce `8 beats//s` when sounded together , find
the speed of sound in the air

Options

A. `33792 cm//s`
B. `35790 cm//s`
C. `31890 cm//s`
D. `40980 cm//s`

Answer

A

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`