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

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 \(beats\) \(/\) \(sec\)

\({=\frac{2}{\lambda}-\left(-\frac{2}{\lambda}\right)=\frac{4}{\lambda}}\)

\({=\frac{2 \times 2}{\frac{320}{800}}\left(\because \lambda=\frac{V}{f}\right)}\)

\( = \frac{{2 \times 2 \times 800}}{{320}} = 10\)