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Two factories are sounding their sirens at 800 $\mathrm{Hz}$. A man goes from one factory to other at a speed of $2 \mathrm{~m} / \mathrm{s}$. The velocity of sound is $320 \mathrm{~m} / \mathrm{s}$. The number of beats heard by the person in one second will be:
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The correct answer is:
10
10
Given: Frequency of sound produced by siren, $f=800 \mathrm{~Hz}$
Speed of observer, $u=2 \mathrm{~m} / \mathrm{s}$
Velocity of sound, $v=320 \mathrm{~m} / \mathrm{s}$
No. of beats heard per second $=$ ?
No. of extra waves received by the observer per second $=\pm 4 \lambda$
$\therefore \quad$ No. of beats/ sec
$$
\begin{aligned}
&=\frac{2}{\lambda}-\left(-\frac{2}{\lambda}\right)=\frac{4}{\lambda} \\
&=\frac{2 \times 2}{\frac{320}{800}} \quad\left(\because \lambda=\frac{V}{f}\right) \\
&=\frac{2 \times 2 \times 800}{320}=10
\end{aligned}
$$
Speed of observer, $u=2 \mathrm{~m} / \mathrm{s}$
Velocity of sound, $v=320 \mathrm{~m} / \mathrm{s}$
No. of beats heard per second $=$ ?
No. of extra waves received by the observer per second $=\pm 4 \lambda$
$\therefore \quad$ No. of beats/ sec
$$
\begin{aligned}
&=\frac{2}{\lambda}-\left(-\frac{2}{\lambda}\right)=\frac{4}{\lambda} \\
&=\frac{2 \times 2}{\frac{320}{800}} \quad\left(\because \lambda=\frac{V}{f}\right) \\
&=\frac{2 \times 2 \times 800}{320}=10
\end{aligned}
$$
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