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:

Both factories emit sound at frequency $$f_0 = 800$$ Hz. The man walks from one factory toward the other at speed $$v_o = 2$$ m/s, while the velocity of sound is $$v = 320$$ m/s. Since both sources are stationary and the observer moves, the Doppler-shifted frequencies are as follows.

For the factory the man approaches, the observed frequency is $$f_1 = f_0\left(\dfrac{v + v_o}{v}\right) = 800 \times \dfrac{322}{320}$$.

For the factory the man moves away from, the observed frequency is $$f_2 = f_0\left(\dfrac{v - v_o}{v}\right) = 800 \times \dfrac{318}{320}$$.

The beat frequency is $$f_1 - f_2 = 800 \times \dfrac{322 - 318}{320} = 800 \times \dfrac{4}{320} = 800 \times \dfrac{1}{80} = 10$$ beats per second.