The Doppler Effect (OCR A Level Physics): Revision Note

The Doppler Effect

• If a wave source is stationary, the wavefronts spread out symmetrically

• If the wave source is moving, the waves can become squashed together or stretched out

  • If the wave source is moving towards an observer the wavefronts will appear squashed

  • If the wavefront is moving away from an observer the wavefronts will appear stretched out

• Therefore, when a wave source moves relative to an observer there will be a change in the observed frequency and wavelength

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

• 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

• Note: Δλ means 'change in wavelength'

  • The actual wavelength emitted by the source remains the same

  • It is only the wavelength that is received by the observer that appears to have changed

• This effect is known as the Doppler effect or Doppler shift

• The Doppler effect is defined as:

   The apparent shift in wavelength occurring when the source of the waves is moving

• The Doppler effect, or Doppler shift, can be observed using any form of electromagnetic radiation

• It can be observed by comparing the light spectrum produced from a close object, such as our Sun, with that of a distant galaxy

  • The light from the distant galaxy is shifted towards the red end of the spectrum (There are more spectral lines in the red end)

  • This provides evidence that the universe is expanding

Comparing the light spectrum produced from the Sun and a distant galaxy

The Doppler Equation

• Doppler shift (Doppler effect) describes how the wavelength (or frequency) of waves change when the source of the waves and observer are moving relative to each other

• If the relative speed between the source of the waves and the observer, ∆v, is small compared to the speed at which the wave is travelling, c, then the Doppler wavelength shift, ∆λ, and frequency shift, ∆f, is given by:

$\frac{∆\lambda }{\lambda }\approx \frac{∆f}{f}\approx \frac{∆v}{c}$

• Where: 

  • Δv = relative speed between source and observer (m s^–1)

  • c = speed of the wave (m s^–1)

  • Δf = observed change in frequency between moving source and stationary source of wave (Hz)

  • f = unshifted frequency of the wave emitted (Hz)

  • Δλ = observed change in wavelength between moving source and stationary source of wave (m)

  • λ = unshifted wavelength of the wave emitted (m)

• The relative speed between source and observer along the line joining them is give by:

∆v = v_s – v_o

• Where:

  • v_s = velocity of electromagnetic waves source

  • v_o = velocity of observer

• Usually, we are calculating the speed of the source of electromagnetic waves relative to an observer which we assume to be stationary

  • Therefore v_o = 0, hence ∆v = v_s = v

  • Where v is the velocity at which the source of the electromagnetic waves is moving from the observer

• Hence, the Doppler shift equation can therefore be written as:

$\frac{∆\lambda }{\lambda }\approx \frac{∆f}{f}\approx \frac{v}{c}$