The frequency of echo will be _____ Hz if the train blowing a whistle of frequency 320 Hz is moving with a velocity of 36 km h$$^{-1}$$ towards a hill from which an echo is heard by the train driver. Velocity of sound in air is 330 m s$$^{-1}$$.

We need to find the frequency of the echo heard by the train driver. The whistle frequency is $$f_0 = 320$$ Hz, the train speed is $$v_s = 36$$ km/h $$= 10$$ m/s, and the speed of sound is $$v = 330$$ m/s.

When the train (the source) moves towards the hill (the observer), the frequency received by the hill is given by the Doppler effect:

$$f_1 = f_0 \times \frac{v}{v - v_s} = 320 \times \frac{330}{330 - 10} = 320 \times \frac{330}{320} = 330 \text{ Hz}$$

The hill then reflects this sound at frequency $$f_1 = 330$$ Hz. Treating the hill as a stationary source and the train driver as a moving observer approaching the source, the frequency of the echo heard by the driver is

$$f_2 = f_1 \times \frac{v + v_o}{v} = 330 \times \frac{330 + 10}{330} = 330 \times \frac{340}{330} = 340 \text{ Hz}$$

Hence, the frequency of the echo heard by the train driver is 340 Hz.