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  4. A tuning fork gives 4 beats with 50 cm length of a sonometer wire. If the length of the wire is shortened by 1 cm the number of beats is still the same. The frequency of the fork is:

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Q. A tuning fork gives $4$ beats with $50 \,cm$ length of a sonometer wire. If the length of the wire is shortened by $1 \,cm$ the number of beats is still the same. The frequency of the fork is:

Jharkhand CECEJharkhand CECE 2002

Solution:

According to law of length of a stretched string
$ n\propto \frac{1}{l} $ or, $ n_{1}l_{1}=n_{2}l_{2} $
Given, $ n_{1}=n-4,n_{2}=n+4,l_{1}=50\,cm, $
$ l_{2}=49\,cm $
Hence, $ (n-4)\times 50=(n+4)\times 49 $
or $ 50 n-200=49n+196 $
or $ n=396\,Hz $