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A column of air at 51 ^(@) C and a tunin...

A column of air at `51 ^(@) C` and a tuning fork p-roduce ` 4 beats//s` when sounded together . As the temperature of air column is decreased the number of beats per second tends to decrease and when temperature is `16^(@)` the two produce ` 1beat//second`. Find the frequency of tuning fork.

Text Solution

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For a given column of air `f prop sqrt(T)`
But as with decrease in temperature beats decrease,
So `Ksqrt((273+51))-f=4.i.e f+4=18K=..(1)`
and `Ksqrt((273+16))-f=1, i.e, f+1=17K...(2)`
So dividing Eqn. (1) by (2) `(f+4)/(f+1)=(18)/(17) or f=50 Hz`
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