Question

A tuning fork $A$ of unknown frequency produces $4$ beats per second when sounded with another tuning fork $B$ of frequency $254\text{Hz}$. When tuning fork $A$ is loaded with wax, it still gives $4$ beats per second with tuning fork $A$. The initial unknown frequency of tuning fork $A$ is

• A. $258\text{Hz}$
• B. $254\text{Hz}$
• C. $250\text{Hz}$
• D. $262\text{Hz}$

Answer 1

The correct option is A $258\text{Hz}$

Given,
$f_b=4\text{Hz}$
We know, beat frequency
$f_b=|f_1-f_2|$
$\Rightarrow f_2=f_1\pm f_b$
Frequency of tuning fork $B$,
$f_1=254\text{Hz}$
$\Rightarrow f_2=254\pm 4\text{Hz}$
So, frequency of tuning fork $A$ can be,
$f_2=250\text{Hz}$ or $258\text{Hz}$
As the tuning fork $A$ is loaded with wax, therefore its time period should increase and frequency should decrease.
So, by intuition, the initial frequency should be $258\text{Hz}$ which will decrease to $250\text{Hz}$ when loaded with wax.