Question

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

• A. $516Hz$
• B. $518Hz$
• C. $508Hz$
• D. $512Hz$

Answer 1

The correct option is A $516Hz$

Step 1: Find the possible frequencies when $2$ beats are produced.

A tuning fork’s frequency is being tested produced $2$ beats with an accurate oscillator at $514Hz$. So, the frequency of running fork may be $512Hz$ or $516Hz$.

Step 2: Find the possible frequencies when $6$ beats are produced.

This also produces a beat of $6Hz$ when oscillator reads $510Hz$. Therefore, frequency of tuning fork may be either $504Hz$ or $516Hz$.

Step 3: Find the actual frequency of fork.

So, let conclude the actual frequency is $516Hz$.

Because $516Hz$ gives $2$ beats per second with $514Hz$ and a beat of $6Hz$ when oscillator reads $510Hz$.

Final Answer: (c)