Question

Two tuning forks $A$ and $B$ produce notes of frequencies $336\text{Hz}$ and $340\text{Hz}$ respectively. An unknown note of guitar string when sounded with fork $A$ produce certain beats. When the same note is sounded with fork $B$, the beat frequency gets doubled. The unknown note of guitar string is -

$($the frequency of guitar string is less than that of $A$ and $B)$

• A. $332\text{Hz}$
• B. $340\text{Hz}$
• C. $344\text{Hz}$
• D. $348\text{Hz}$

Answer 1

The correct option is A $332\text{Hz}$

$n_A=336\text{Hz}$

$n_B=340\text{Hz}$

Let unknown frequency is $n$.

It produces $\Delta n$ beats with $A$.

$n_A–n=\Delta n...\left(I\right)$

$n_B–n=2\Delta n...\left(II\right)$

Subtracting $I$ from $II$,

$n_B–n_A=\Delta n$

$\Rightarrow 340-336=\Delta n$

$\therefore \Delta n=4$

Now,

$n=n_A-\Delta n$

$\Rightarrow n=336–4=332\text{Hz}$