Question

When two tuning forks $A$ and $B$ are sounded together, the number of beats heard is $\nu$. The frequency of fork $A$ is $f$. If the prong of fork $B$ is loaded with a little wax, the number of beats decreases. The initial frequency of fork $B$ is

• A. $f+\nu$
• B. $f-\nu$
• C. $f+2\nu$
• D. $f-2\nu$

Answer 1

The correct option is A $f+\nu$

Let $f_0$ be the initial frequency of fork $B$.
Number of beats heard per second is $\nu$, when fork $A$ and $B$ are sounded together.
$\Rightarrow f_B=|f_A-f_0|=v$
$\Rightarrow f_0=f+\nu$ or $f-\nu$
When fork $B$ is loaded with wax, its frequency decreases. However it is given that beat frequency also decreases.
Considering $f_0$ to be $f-\nu$, it will further reduce after waxing. Therefore beat frequency increase i.e $f_B>\nu$
Again, considering $f_0$ to be $f+\nu$, it will further reduce after waxing. Therefore beat frequency decreases i.e $f_B<\nu$
$\therefore \left(a\right)$ is the correct answer.