When an air column at `27^(@)C` and a tuning fork are sounded together, 5 beats per second are produced. The frequency of the fork is less than that of air column. No beat is heard at `-3^(@)C`. Determine the frequency of the fork.

Explanation

Let the frequency of tuninig fork be v. Therefore, frequency of air column at `27^(@)C=(v+5)`
As no beat is heard at `-3^(@)C`, therefore, frequency of air column at `-3^(@)C=v`
`:. (v+5)/(v)=(upsilon_(26^(@)C))/(upsilon_(-3^(@)C))`
`=sqrt((273+27)/(273-3))=sqrt((300)/(270))`
`1+(5)/(v)=(1+(1)/(9))^(1//2)=1+(1)/(18)`
`v=5xx18=90Hz`