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Q. A tuning fork whose frequency as given by manufacturer is $512\, Hz$ is being tested with an accurate oscillator. It is found that the fork produces a beat of $2\, Hz$ when oscillator reads $514\, Hz$ but produces a beat of $6\, Hz$ when oscillator reads $510\, Hz$. The actual frequency of fork is

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Solution:

The tuning fork whose frequency is being tested produces 2 beats with oscillator at $514\, Hz$, therefore, frequency of tuning fork may either be 512 or $516 .$ With oscillator frequency 510 it gives 6 beats/sec, therefore frequency of tuning fork may be either 516 or 504 .Therefore, the actual frequency is $516\, Hz$ which gives 2 beats/sec with $514\, Hz$ and 6 beats/sec with $510\, Hz$.