Question

A tuning fork produces $4$ beats per second with another tuning fork of frequency $266\text{Hz}$. The first one is now loaded with wax and the beat frequency is found to be $8$ per second. What is the original frequency of the first tuning fork ?

• A. $270\text{Hz}$
• B. $266\text{Hz}$
• C. $262\text{Hz}$
• D. $274\text{Hz}$

Answer 1

Answer: (A), (C)

$262\text{Hz}$

Given that $f_2=266\text{Hz}$
Beat frequency $=|f_1-f_2|=4$
$\Rightarrow f_1=262\text{Hz or}270\text{Hz}$


Case (i)
Let $f_1=262\text{Hz}$
Now, as first tuning fork is loaded, $f_1$ reduces.
If $f_1$ reduces to $258\text{Hz}$, we can hear beat frequency of $8$ per second with $f_2$.

Case (ii)
Let $f_1=270\text{Hz}$
Now as first tuning fork is loaded, $f_1$ reduces.
If $f_1$ reduces to $258\text{Hz}$, we can hear beat frequency of $8$ per second with $f_2$.

Options $\left(a\right),\left(c\right)$ are correct.