A tuning fork gives 3 beats per second with sonometer wire when its length is either 49.8cm or 50.2cm. Find the frequency of the tuning fork.

Let v be the frequency of tuning fork.

Let, v₁ and v₂ be the frequencies of sonometer wire when its length is 49.8cm and 50.2 cm respectively.

The frequency of sonometer wire is inversely proportional to the length of the sonometer wire.

Therefore,

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From the above equation, it is clear that v₁ > v₂.

Since tuning fork produces 3 beats per second with sonometer wire for both lengths, therefore