Two factories are sounding their sirens at $800\, Hz$ . A man goes from one factory to other at a speed of $2\,m/s$. The velocity of sound is $320\, m/s$. The number of beats heard by the person in one second will be
JEE MAIN 2014, Medium
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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 $=\pm 4 \lambda$
$\therefore \quad$ $Na$ of $beats$ $/$ $sec$
${=\frac{2}{\lambda}-\left(-\frac{2}{\lambda}\right)=\frac{4}{\lambda}}$
${=\frac{2 \times 2}{\frac{320}{800}}\left(\because \lambda=\frac{V}{f}\right)}$
$ = \frac{{2 \times 2 \times 800}}{{320}} = 10$
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