Question

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

• A. $342\text{Hz}$
• B. $335\text{Hz}$
• C. $338\text{Hz}$
• D. $345\text{Hz}$

Answer 1

The correct option is B $335\text{Hz}$

Suppose the frequency of fork $A$ is $f$.

Then, $f\pm 340=5$

$\Rightarrow f=335\text{Hz}$ or $345\text{Hz}$

Now, after filing, suppose the frequency of fork $A$ is $f^{{}^{\prime }}$.

Then, $f^{{}^{\prime }}\pm 340=2$

$\Rightarrow f^{{}^{\prime }}=338\text{Hz}$ or $342\text{Hz}$

After filing, time period decreases slightly and frequency increases slightly.

Therefore, frequency of fork $A$ increases from $335\text{Hz}$ to $338\text{Hz}$.

Hence, original frequency is $335\text{Hz}$.