The Doppler Effect (HL IB Physics)

• When a source of sound, such as the whistle of a train or the siren of an ambulance, moves away from an observer:
  • It appears to decrease in frequency, i.e. it sounds lower in pitch
  • The source of the sound however, remains at a constant frequency
• This frequency change due to the relative motion between a source of sound or light and an observer is known as the Doppler effect (or Doppler shift)
• When the observer and the source of sound (e.g. ambulance siren) are both stationary:
  • The waves appear to remain at the same frequency for both the observer and the source
• When the observer and the source of sound (e.g. ambulance siren) are moving relative to each other
  • The waves appear to have a different frequency for both the observer and the source

Stationary source and observer. The wavelength of the waves are the same for both observers

• When the source starts to move towards the observer, the wavelength of the waves is shortened
  • The sound, therefore, appears at a higher frequency to the observer

Moving source at speed v_s and stationary observer. The waves are closer together closer near the stationary observer

• Notice how the waves are closer together between the source and the observer compared to point P and the source
• This also works if the source is moving away from the observer
  • If the observer was at point P instead, they would hear the sound at a lower frequency due to the wavelength of the waves broadening

• The frequency is increased when the source is moving towards the observer
• The frequency is decreased when the source is moving away from the observer

• The same phenomena occurs for electromagnetic waves, such as light

• Waves moving away from the observer are red-shifted
  • Their wavelengths shift to the red end of the electromagnetic spectrum
  • This is equivalent to sound waves appearing at a lower frequency to the observer
• Waves moving towards the observer are blue-shifted
  • Their wavelengths shift to the blue end of the electromagnetic spectrum
  • This is equivalent to sound waves appearing at a higher frequency to the observer
• This is because red light has a longer wavelength than blue light

Red shift and blue shift for electromagnetic waves

• Wavefront diagrams help visualise the Doppler effect for moving wave sources and stationary observers

Wavefronts are even in a stationary object but are squashed in the direction of the moving wave source

• Δλ is the change in wavelength
  
  • The bigger the change, the bigger the doppler shift
• A moving object will cause the wavelength, λ, (and frequency) of the waves to change:
  • The wavelength of the waves in front of the source decreases (λ – Δλ) and the frequency increases
  • The wavelength behind the source increases (λ + Δλ) and the frequency decreases

• The Doppler shift is observed by all waves including sound and light