An observer is riding on a bicycle and moving towards a hill at 18… | JEE Main 2022 (25 Jul, Shift 1)

Q42JEE Main 2022 · 25 JUL · SHIFT 1Difficult

Doppler Effect

An observer is riding on a bicycle and moving towards a hill at $18\text{ kmh}^{-1}$ . He hears a sound from a source at some distance behind him directly as well as after its reflection from the hill. If the original frequency of the sound as emitted by source is $640\text{ Hz}$ and velocity of the sound in air is $320\text{ m/s}$ , the beat frequency between the two sounds heard by observer will be _____________ $\text{Hz}$ .

Numerical answer type. Work it out, then open the answer.

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Answer: 20

Observer speed $u = 18$ km/h $= 5$ m/s, towards the hill and away from the source.
Direct sound (observer moving away): $f_1 = 640 \times \frac{320 - 5}{320} = 630$ Hz
Reflected sound reaches the hill at $640$ Hz (hill at rest); observer moves towards it: $f_2 = 640 \times \frac{320 + 5}{320} = 650$ Hz
Beat frequency $= 650 - 630 = 20$ Hz

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