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:

Solution :
Frequency of sound produced by siren,
$$f = 800\,Hz$$
Speed of observer, $$u = 2\,m/s$$
Rigid support Velocity of sound, $$v = 320\,m/s$$
As we know No. of beats heard per second = ?
No. of extra waves received by the observer per second $$ = \pm 4\lambda $$
$$\eqalign{ & \therefore {\text{No}}{\text{.}}\,{\text{of}}\,{\text{beats}}/\sec \cr & = \frac{2}{\lambda } - \left( { - \frac{2}{\lambda }} \right) = \frac{4}{\lambda } \cr & = \frac{{2 \times 2}}{{\frac{{320}}{{800}}}} = \frac{{2 \times 2 \times 800}}{{320}} = 10\,\,\left( {\because \lambda = \frac{V}{f}} \right) \cr} $$