Question

Two tuning forks have frequencies $380$ and $384Hz$ respectively. When they are sounded together, they produce $4$ beats. After hearing the maximum sound, how long will it take to hear the minimum sound

• A. $\frac{1}{4}sec$
• B. $\frac{1}{16}sec$
• C. $\frac{1}{8}sec$
• D. $\frac{1}{2}sec$

Answer 1

The correct option is C $\frac{1}{8}sec$

Given, two tuning forks $n_1$ and $n_2$ having frequency,
$\Rightarrow n_1=380Hz$
$\Rightarrow n_2=384Hz$

When they are sounded together, they produce $4$ beats.

$\Rightarrow \text{Beat period}=\frac{1}{n_2-n_1}$
$=\frac{1}{384-380}$
$\Rightarrow \text{Beat period}=\frac{1}{4}sec$

Therefore, minimum time interval between maxima and minima,
$\Rightarrow t=\frac{T}{2}=\frac{1}{4\left(2\right)}=\frac{1}{8}sec$

$\therefore$ After hearing the maximum sound, it will take to hear the minimum sound in
$\frac{1}{8}s$.

Final Answer: (c)