Question

Two factories are sounding their sirens at $800Hz$. A man goes from one factory to another at a speed of $2m/s$. The velocity of sound is $320m/s$. The number of beats heard by the person in one second will be.

Answer 1

Step 1: Given data

$v_o$ = $2\raisebox{1ex}{$M$}\!\left/ \!\raisebox{-1ex}{$S$}\right.$

$n$= $800Hz$

$v_s$ = $320\raisebox{1ex}{$M$}\!\left/ \!\raisebox{-1ex}{$S$}\right.$

Step 2: Write the formula

A number of beats per second are given by the formula: $\mathit{b}\mathbf{}\mathbf{=}\frac{\mathbf{2}\mathbf{\times }{\mathbf{v}}_{\mathbf{o}}\mathbf{\times }\mathbf{n}}{{\mathbf{v}}_{\mathbf{s}}}$

Where,

$b$= number of beats per second

$v_o$= speed of the observer

$n$ = Actual frequency of the source

$v_s$= Velocity of the sound

Step 3: Calculate the number of beats per second.

Replacing these values in the formula we get,

$$\begin{gathered} b=\frac{2\times v_o\times n}{v_s} \\ b=\frac{2\times 2\times 800}{320} \\ b=10Hz \end{gathered}$$

Therefore, the number of beats heard by the person in one second will be $\mathbf{10}\mathbf{}\mathit{H}\mathit{z}$.