JEE Main · 2022 · 25 Jul 2022 · Shift 1 · Waves & Sound

An observer is riding on a bicycle and moving towards a hill at

18 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 Hz and velocity of the sound in air is

320 m / s

, the beat frequency between the two sounds heard by observer will be

____

Hz.

Answer: 20

Solution

The observer moves at

v_{o b} = 18 km/h = 5 m/s

toward the hill.

Direct sound (observer moving away from source): Using the Doppler formula with observer moving away from a stationary source:

f_{direct} = (\frac{v - v _{o b}}{v}) f_{0} = (\frac{320 - 5}{320}) \times 640 = 630 Hz

Reflected sound (observer moving toward the hill, which acts as a source): The hill reflects the sound, and the observer moves toward it:

f_{reflected} = (\frac{v + v _{o b}}{v}) f_{0} = (\frac{320 + 5}{320}) \times 640 = 650 Hz

Beat frequency:

f_{beat} = f_{reflected} - f_{direct} = 650 - 630 = 20 Hz

JEE Main · 2022 · 25 Jul 2022 · Shift 1 · Integer answer

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JEE Main · 2022 · 25 Jul 2022 · Shift 1 · Waves & Sound

Solution

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