Question

A tuning fork $A$ when sounded with a tuning fork $B$ of frequency $480\text{Hz}$ produces $5$ beats per second. When the prongs of $A$ are loaded with wax, it gives $3$ beats per second. The original frequency of the tuning fork $A$ is:

• A. $475\text{Hz}$
• B. $485\text{Hz}$
• C. $483\text{Hz}$
• D. $477\text{Hz}$

Answer 1

The correct option is B $485\text{Hz}$

Given: $f_B=480\text{Hz}$
Beat frequency observed on sounding both forks is $5\text{Hz}$
$\Rightarrow f_A=485\text{Hz}$ or $475\text{Hz}$
If the intial frequency of $A$ is $475\text{Hz}$ and it reduces further due to waxing, the beat frequency will increase. $(\because f_B=480\text{Hz})$

However, the beat frequency is decreasing to $3\text{Hz}$, which is only possible if the initial frequency of the fork $A$ is $485\text{Hz}$
Thus, it is feasible to get $3$ beats per second, when $f_A\downarrow$ to $483\text{Hz}$ after waxing.
$\therefore f_A=485\text{Hz}$