# The Doppler Effect(OCR A Level Physics)

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Katie M

Expertise

Physics

## 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:

• 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 = vs vo

• Where:
• vs = velocity of electromagnetic waves source
• vo = 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 vo = 0, hence ∆v = vs = 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:

#### Worked example

A stationary source of light is found to have a spectral line of wavelength 438 nm.  The same line from a distant star that is moving away from us has a wavelength of 608 nm.

Calculate the speed at which the star is travelling away from Earth.

Step 1: List the known quantities

• Unshifted wavelength = λ = 438 nm = 438 × 10–9 m
• Shifted wavelength = 608 nm = 608 × 10–9 m
• Change in wavelength = ∆λ = (608 – 438) × 10–9 = 170 × 10–9
• Speed of light = c = 3.00 × 108 m s–1

Step 2: State the Doppler shift equation

Step 3: Substitute values to calculate v

v = = 1.16 × 108 m s–1

#### Exam Tip

You need to know that in the visible light spectrum red light has the longest wavelength and the smallest frequency compared to blue light which has a shorter wavelength and higher frequency.

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