doppler effect questions with solutions

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• NumericeasyWave Motiondoppler effect

  A source of frequency 300 Hz moves through still air at 30 m/s. The speed of sound is 330 m/s. If the wavelength immediately ahead of the moving source is N metres, find N.

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• MCQmediumWave Motiondoppler effect

  A source of frequency f moves through still air with speed uₛ < v, where v is the speed of sound. Which pair correctly gives the wavelengths immediately in front of and behind the moving source?

  Options

  • Option A

    λ₁ = (v-uₛ)/f and λ₂ = (v+uₛ)/f

  • Option B

    λ₁ = (v+uₛ)/f and λ₂ = (v-uₛ)/f

  • Option C

    λ₁ = λ₂ = v/f

  • Option D

    λ₁ = v/(f-uₛ) and λ₂ = v/(f+uₛ)

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• MCQmediumWave Motiondoppler effect

  A sound source moves with constant speed on a circle whose centre is occupied by a stationary observer. The source emits a constant frequency f. Neglect wind and relativistic effects. What frequency is heard by the observer?

  Options

  • Option A

    Always greater than f

  • Option B

    Always less than f

  • Option C

    Alternately greater and smaller than f

  • Option D

    Exactly f throughout the motion

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• NumericmediumWave Motiondoppler effect

  A stationary observer hears a moving source at 360 Hz while it approaches and at 300 Hz after it has passed and is receding. The speed of sound is 330 m/s. If the source speed is N m/s, find N.

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• A/RmediumWave Motiondoppler effect

  Choose the correct option for the following Assertion (A) and Reason (R).

  Assertion

  When a moving source hears its own sound after reflection from a stationary wall, the received echo frequency involves two Doppler factors.

  Reason

  The stationary wall first receives a Doppler-shifted frequency from the moving source, and the moving source then acts as an observer for the reflected wave.

  Options

  • Option A

    Both A and R are true and R is the correct explanation of A.

  • Option B

    Both A and R are true but R is NOT the correct explanation of A.

  • Option C

    A is true but R is false.

  • Option D

    A is false but R is true.

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• NumericdifficultWave Motiondoppler effect

  An audio transmitter T and receiver R are suspended from identical 8 m strings. They are displaced in opposite horizontal directions by θ₀ = cos⁻¹(0.9) and released together. The transmitter frequency is 660 Hz and sound speed is 330 m s⁻¹. With g = 10 m s⁻², find the maximum variation in received frequency in hertz.

  

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• Multi-correctmediumWave Motiondoppler effect

  A source of frequency f moves through still air with speed uₛ < v. Which statements are correct?

  Select all that apply

  • Option A

    The wavelength in front is (v-uₛ)/f.

  • Option B

    The wavelength behind is (v+uₛ)/f.

  • Option C

    The source continues to oscillate at frequency f in its own frame.

  • Option D

    A stationary observer in front of the approaching source hears a frequency greater than f.

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• MCQmediumWave Motiondoppler effect

  A sound source moves uniformly on a large circular path with speed u. A stationary observer is so far from the circle that the line of sight may be treated as fixed. What is the ratio of the maximum to the minimum observed frequency?

  Options

  • Option A

    (v-u)/(v+u)

  • Option B

    (v+u)/(v-u)

  • Option C

    v²/(v²-u²)

  • Option D

    (v+u)/v

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• NumericmediumWave Motiondoppler effect

  A source emitting 320 Hz moves directly towards a stationary wall at 20 m/s. The speed of sound is 340 m/s. The source compares the echo with its own emitted sound. If the beat frequency is N Hz, find N.

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• MCQmediumWave Motiondoppler effect

  Car P moves at 20 m s⁻¹ and sounds a 400 Hz horn. Car Q is behind P, moving in the same direction at 40 m s⁻¹. Take sound speed 360 m s⁻¹. The frequency heard in Q is approximately:

  Options

  • Option A

    471 Hz

  • Option B

    514 Hz

  • Option C

    421 Hz

  • Option D

    485 Hz

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