The Doppler Effect

This lesson covers the Doppler effect for both sound and light, and its importance in astronomy, as required by the AQA GCSE Physics specification (4.8.2). This is a Physics-only topic. You need to understand what the Doppler effect is, how it applies to sound waves and electromagnetic waves, and how it provides evidence for the expansion of the universe through red-shift.

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What Is the Doppler Effect?

The Doppler effect is the change in the observed frequency (and wavelength) of a wave when the source of the wave is moving relative to the observer. It was first described by the Austrian physicist Christian Doppler in 1842.

The Doppler effect applies to all types of waves, including sound waves, light waves, and other electromagnetic waves.

Key Principle

• When a wave source moves towards an observer, the observed wavelength is shorter (compressed) and the observed frequency is higher.
• When a wave source moves away from an observer, the observed wavelength is longer (stretched) and the observed frequency is lower.
• The wave source itself does not change — it is only the observed frequency and wavelength that change due to the relative motion.

Exam Tip: The Doppler effect is about relative motion between the source and the observer. It does not matter whether the source is moving and the observer is stationary, or the observer is moving and the source is stationary — the effect is the same. What matters is the relative velocity between them.

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The Doppler Effect for Sound

The most familiar example of the Doppler effect is the change in pitch of a siren as an emergency vehicle passes you.

Example: An Ambulance Siren

1. As the ambulance approaches you, the sound waves are compressed — the wavelength is shorter and the frequency is higher. You hear a higher pitch.
2. As the ambulance passes and moves away from you, the sound waves are stretched — the wavelength is longer and the frequency is lower. You hear a lower pitch.
3. The siren itself is producing sound at a constant frequency — it is only the observed frequency that changes.

Situation	Wavelength	Frequency	Pitch
Source moving towards observer	Shorter (compressed)	Higher	Higher
Source stationary relative to observer	Normal	Normal	Normal
Source moving away from observer	Longer (stretched)	Lower	Lower

How It Works

When the source moves towards the observer, each successive wave crest is emitted from a position slightly closer to the observer than the previous one. This means the wave crests are bunched together — the wavelength is shorter and the frequency is higher.

When the source moves away, each wave crest is emitted from slightly further away, so the crests are spread apart — the wavelength is longer and the frequency is lower.

graph LR
    A["Source Moving Left"] --> B["Compressed Waves (shorter wavelength, higher frequency)"]
    A --> C["Stretched Waves (longer wavelength, lower frequency)"]
    B --> D["Observer on Left: hears higher pitch"]
    C --> E["Observer on Right: hears lower pitch"]

    style A fill:#e67e22,color:#fff
    style B fill:#3498db,color:#fff
    style C fill:#e74c3c,color:#fff

Exam Tip: When describing the Doppler effect for sound, always mention: (1) the source is moving relative to the observer, (2) the waves are compressed/stretched, (3) the observed frequency increases/decreases, and (4) the actual frequency emitted by the source does not change. A complete answer must include all four points.

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The Doppler Effect for Light

The Doppler effect also applies to electromagnetic waves, including visible light. This is crucial for astronomy.

Blue-Shift

When a light source (such as a star or galaxy) moves towards an observer, the light waves are compressed:

• The observed wavelength is shorter.
• The light is shifted towards the blue end of the visible spectrum.
• This is called blue-shift.

Red-Shift

When a light source moves away from an observer, the light waves are stretched:

• The observed wavelength is longer.
• The light is shifted towards the red end of the visible spectrum.
• This is called red-shift.

Motion of Source	Effect on Wavelength	Effect on Frequency	Shift
Towards observer	Shorter	Higher	Blue-shift
Away from observer	Longer	Lower	Red-shift

Application to Galaxies

Edwin Hubble observed that the light from nearly all distant galaxies is red-shifted. This means that nearly all galaxies are moving away from us. Furthermore, more distant galaxies show greater red-shift, meaning they are receding faster.

This observation provides the key evidence that the universe is expanding — the space between galaxies is stretching, carrying the galaxies apart and stretching the light waves in transit.

Exam Tip: Red-shift and blue-shift are specific applications of the Doppler effect to light. The Doppler effect is the underlying physical phenomenon; red-shift is the observed result when galaxies are moving away from us. If asked to "explain red-shift using the Doppler effect," link them explicitly: the Doppler effect causes the wavelength of light to increase (shift to red) when the source moves away from the observer.

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Connecting the Doppler Effect to the Big Bang

The Doppler effect is the mechanism that allows us to detect the motion of distant galaxies. The chain of reasoning is:

1. The Doppler effect means that light from a receding source has a longer wavelength (red-shifted).
2. Observations show that the light from nearly all distant galaxies is red-shifted.
3. This means nearly all galaxies are moving away from us.
4. More distant galaxies have greater red-shift, meaning they are receding faster (Hubble's Law).
5. This implies the universe is expanding.
6. Tracing the expansion backwards suggests the universe began from a single, extremely hot, dense point — the Big Bang.

graph TD
    A["Doppler Effect"] --> B["Light from receding galaxies is red-shifted"]
    B --> C["Nearly all galaxies show red-shift"]
    C --> D["Galaxies are moving away from us"]
    D --> E["More distant galaxies recede faster (Hubble’s Law)"]
    E --> F["The universe is expanding"]
    F --> G["Tracing back: the Big Bang"]

    style A fill:#9b59b6,color:#fff
    style B fill:#e74c3c,color:#fff
    style F fill:#2ecc71,color:#fff
    style G fill:#e67e22,color:#fff

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The Doppler Effect in Everyday Life

Beyond astronomy, the Doppler effect has practical applications:

Application	How It Uses the Doppler Effect
Speed cameras (radar guns)	A radar gun emits radio waves at a moving vehicle. The reflected waves are Doppler-shifted. The change in frequency is used to calculate the vehicle's speed.
Medical ultrasound (Doppler scan)	Ultrasound waves reflected from moving blood cells are Doppler-shifted. This allows doctors to measure the speed and direction of blood flow.
Weather radar	Radio waves reflected from raindrops are Doppler-shifted. This allows meteorologists to measure wind speeds and detect rotation in storms (e.g., tornadoes).
Astronomy	Red-shift of spectral lines tells astronomers how fast galaxies and stars are moving relative to Earth.

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Calculating the Doppler Effect (Higher Tier)

For Higher Tier, you may need to use the following relationships:

The observed change in wavelength due to the Doppler effect is:

change in wavelength / original wavelength = v / c

where:

• v = speed of the source relative to the observer (m/s)
• c = speed of the wave (m/s) — for light, c = 3 x 10 to the power 8 m/s

Similarly, the change in frequency:

change in frequency / original frequency = v / c

These equations are only valid when v is much less than c (i.e., for speeds much less than the speed of light).

Worked Example

A galaxy has a spectral line that should be at a wavelength of 500 nm but is observed at 505 nm. Calculate the speed of recession.

Step 1: Change in wavelength = 505 - 500 = 5 nm