When the air column of aresonance tube is vibrated together with a tuning fork 3 beats are heard per second either the temperature of the air columns is `51^(@) C` or `16^(@)` C the frequency of the tuning fork is

Answer

c

Explanation

Number of beats per second when that air column of resonance tube n=3
If n be frequency of tuning fork
Then `n prop sqrt(T ) [ T to` temperature
`(n_(1))/( n_(2)) = sqrt((T_(1))/(T_(2))`
At `51^(@) C, T_(1) = 273 + 51 = 324 k`
`n_(1) = n +3` { frequency of tuning fork increase at the higher temperature }
At `16^(@)C, T = 273 + 16 = 289 K`
`n_(2) = n-3` [At lower temperature frequency of the tuning fork decrease ]
`(n_(1))/(n_(2)) = sqrt((324)/(298)) rArr (n+3)/( n-3) = (18)/(17)`
`18n - 54 = 17n + 51`
`rArr 18 n - 17n = 54 + 51 rArr n =105 Hz`