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A tuning fork and an air column whose te...

A tuning fork and an air column whose temperature is ` 51^(@)C` produce 4 beats in one second, when sounded together . When the temperature of air column decreases . When the temperature remain `16^(@)C` only one beat per second is produced. The frequency of the tuning fork is

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For a given air column.
`n prop V` and `V prop sqrtT`
`rArr n prop sqrtT` or `n=KsqrtT`
If frequency of fork is `n_0`
`n_0-KsqrtT=4 `or `KsqrtT-n_0=4`
But as with decrease in temperature beats decrease , first choice is not permissible .
`Ksqrt((273+51))-n_0=4 ` i.e., `n_0+4=18K`...(1)
`Ksqrt((273+16))-n_0=1` i.e. `n_0+1 =17K`. ...(2)
Solving (1)and (2) we get
`n_0` =50 Hz
k=5
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