Doppler Effect for Sound Waves

2026 Syllabus Objectives

By the end of this topic, you should be able to:

  1. Understand that when a source of sound waves moves relative to a stationary observer, the observed frequency is different from the source frequency
  2. Use the expression fo = fs v / (v ± vs) for the observed frequency when a source of sound waves moves relative to a stationary observer

What is the Doppler Effect?

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The Doppler effect is the change in the frequency (pitch) of a sound wave that you hear when the source of the sound is moving towards you or away from you.

Everyday examples:

  • When an ambulance with its siren on drives towards you, the siren sounds higher pitched (higher frequency)
  • As the ambulance drives away from you, the siren sounds lower pitched (lower frequency)
  • The same thing happens with a train whistle or a racing car engine

The actual frequency of the ambulance siren doesn't change – it's always emitting the same frequency. But you hear a different frequency because of the movement.

Why Does the Doppler Effect Happen?

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To understand this, imagine sound waves spreading out from a source like ripples on a pond.

When the source is stationary:

If both the source and you (the observer) are not moving, the sound waves spread out evenly in all directions. The distance between each wave (the wavelength) is the same in every direction. You hear the sound at its actual frequency.

When the source moves towards you:

When the source moves towards you, something interesting happens:

  • The source emits waves as it moves
  • Each new wave is emitted from a position closer to you than the previous wave
  • This means the waves get squashed or compressed together in front of the source
  • The wavelength becomes shorter in the direction of motion

Since the speed of sound stays the same, but the wavelength is shorter:

  • Using the wave equation: v = fλ (speed = frequency × wavelength)
  • If wavelength (λ) decreases and speed (v) stays constant, frequency (f) must increase
  • You hear a higher frequency (higher pitch)

When the source moves away from you:

The opposite happens:

  • Each new wave is emitted from a position further away than the previous wave
  • The waves get stretched or spread out behind the source
  • The wavelength becomes longer

Since wavelength is longer but speed stays constant:

  • Frequency must decrease
  • You hear a lower frequency (lower pitch)

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