Question

A tuning fork $A$ of unknown frequency produces $5\frac{beats}{sec}$ with a fork of known frequency $340Hz$. When fork $A$ is filed, the beat frequency decreases to$2\frac{beats}{sec}$. What is the frequency of fork $A$?

• A. $342Hz$
• B. $335Hz$
• C. $338Hz$
• D. $345Hz$

Answer 1

The correct option is B

$335Hz$

Step 1. Data Given:

Frequency of the second fork $f_B=340Hz$

Beats produced before the filing of Fork $A$, $b_1=5\frac{beats}{sec}$

Beats produced after the filing of Fork $A$, $b_2=2\frac{beats}{sec}$

Step 2. Find the frequency of Fork $\mathit{A}$:

For the production of $5\frac{beats}{sec}$ the possible frequencies of $A$ can be

$f_A=340\pm 5Hz$

$f_A=345or335Hz$

Now, filing increases the frequency of the Fork $A$,

For the production of $2\frac{beats}{sec}$the difference between the frequencies of the fork $A$ and the second fork should be minimum.

If we consider $345Hz$, then the increase in the frequency of Fork $A$, due to filing, will increase the difference between the two forks.

$\Rightarrow$ $335Hz$ is the most probable answer.

Hence option (B) is correct.