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MCQEasyJEE 2023Doppler Effect

JEE Physics 2023 Question with Solution

The engine of a train moving with speed 10 m s−110 \, \text{m s}^{-1} towards a platform sounds a whistle at frequency 400 Hz400 \, \text{Hz}. The frequency heard by a passenger inside the train is (neglect air speed, speed of sound in air = 330 m s−1330 \, \text{m s}^{-1}):

  • A

    400 Hz400 \, \text{Hz}

  • B

    388 Hz388 \, \text{Hz}

  • C

    200 Hz200 \, \text{Hz}

  • D

    412 Hz412 \, \text{Hz}

Answer

Correct answer:A

Step-by-step solution

Standard Method

Given: The train engine and the passenger are inside the same train. The whistle frequency is 400 Hz400 \, \text{Hz}.

Find: The frequency heard by the passenger inside the train.

For a passenger moving together with the source, there is no relative motion between the source and the observer. Therefore, Doppler shift does not occur for the sound heard inside the train.

So, the observed frequency remains equal to the actual frequency:

f′=f=400 Hzf' = f = 400 \, \text{Hz}

Common mistakes

  • Applying the Doppler effect for a passenger inside the train as if the observer were standing on the platform is incorrect, because the passenger and the source move together. Use relative motion between source and observer, not motion relative to the ground.

  • Using the speed of sound value to calculate a shifted frequency here is unnecessary. Since there is no relative motion between the whistle and the passenger, the speed of sound does not affect the final observed frequency in this case.

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