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Question:

A siren emitting a sound of frequency 800Hz moves away from an observer towards a cliff at a speed of 15ms⁻¹. Then, the frequency of sound that the observer hears in the echo reflected from the cliff is (Take velocity of sound in air = 330ms⁻¹)

800Hz

885Hz

765Hz

838Hz

Solution:

The general formula for apparent frequency is f'=v±vO/v∓vS
As observer is at rest so vO=0
Since the source moves towards cliff, i.e., effectively the source moves towards the observer (the sound being heard through echo), so vS taken as -vS=15 m/s
Thus, f'=v/(v-vS)f = 330/(330-15)800 = 838 Hz