Question

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

Answer 1

Step 1: Given data

First frequency of tuning fork$\left(f_1\right)=\text{380 Hz}$

Second frequency of tuning fork$\left(f_2\right)=\text{384 Hz}$

Step 2: To find

Time is required to hear the minimum sound.

Step 3: Formula used

The time interval between two consecutive peaks or minima is called the beat period. It is also equivalent to the beat frequency reciprocal.

$\text{Beat period}=\frac{1}{f_2-f_1}$

$\text{Time period=}\frac{\text{Beat period}}{2}$

Step 4: Calculate the time required to hear the minimum sound

$$\begin{gathered} \text{Beat period}=\frac{1}{\text{384 Hz-380 Hz}} \\ =\frac{1}{4\text{Hz}} \\ =\frac{1}{4}\text{seconds} \end{gathered}$$

$$\begin{gathered} \text{Time period}=\frac{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}\text{seconds}}{2} \\ =\frac{1}{8}\text{seconds} \\ =0.125\text{seconds} \end{gathered}$$

Hence, the required time is $0.125\text{seconds}$.