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

Explanation

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