Edexcel IGCSE Physics · Spec 3.1-3.8
Wave Properties and the Doppler Effect
Covers compare transverse and longitudinal waves, Use wave measurements and the wave equation correctly and Explain wavefronts and the Doppler effect.
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Wave Properties and the Doppler Effect
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Explained
Wavefronts, and what moving the source does to them
A wavefront is a line joining points on a wave that are all in the same phase, so all the crests joined together, or all the troughs. Drawing waves as a series of parallel wavefronts, seen from above, is what makes the Doppler effect possible to explain.
The distance between two adjacent wavefronts is the wavelength. So anything that changes the spacing of the wavefronts has changed the wavelength, and that is the whole mechanism of this topic.
The quantities, briefly
Amplitude is the maximum displacement from the rest position, measured from the middle to a peak rather than from peak to trough.
Wavelength is the distance between two corresponding points on adjacent waves.
Frequency is the number of complete waves passing a point each second, measured in hertz.
Period is the time for one complete wave, and it is one divided by the frequency.
Wave speed equals frequency multiplied by wavelength. In a given medium the speed is fixed, so frequency and wavelength are inversely proportional: if one rises the other must fall.
The Doppler effect
When a source moves towards you, it travels a little way after emitting each wavefront and before emitting the next, so it emits each one from slightly closer to you. The wavefronts ahead of it are therefore squeezed together.
Closer wavefronts mean a shorter wavelength. The wave speed has not changed, because the medium has not changed, so a shorter wavelength must mean a higher frequency. You hear a higher pitch.
Behind the source the opposite happens. The wavefronts are stretched apart, the wavelength is longer, the frequency is lower, and the pitch drops.
That is why a siren changes note as it passes rather than as it approaches. The pitch is steady and high while coming towards you, steady and low once past, and the change happens at the moment of passing.
Two things are worth guarding here. The source is not producing a different note; it emits the same frequency throughout, and only the observer hears a difference. And the wave speed does not change, which is what forces the frequency to change instead.
What the mark scheme accepts and rejects
An Edexcel International GCSE Physics mark scheme awards four marks for explaining a Doppler shift in a ripple tank, and the four points are worth learning as a fixed order: the frequency is greater; the wavefronts, peaks or crests are closer together; the wavelength decreases; and the wave speed does not change.
Its notes allow wavefronts more bunched up or compressed. And then, one line later, it instructs the examiner to ignore the phrase the wave is compressed.
Those look almost identical and they say different things. Wavefronts closer together describes the spacing between them, which is what changed. The wave is compressed describes the wave itself as squashed, which it is not, and it also collides with the word compression from longitudinal waves, where it means something else again.
The final marking point is the one most often missing. Stating that the wave speed does not change is what turns the answer into an explanation, because a shorter wavelength only forces a higher frequency if the speed is fixed. Without it you have described what happened and not why.
The mark scheme also ignores references to the speed of the dipper, which is the thing being moved. The explanation is about the waves it produces, not about the object.
A parallel mark scheme takes the same reasoning underwater, with whales, and lays out three marks in the same shape: the wavefronts are compressed and the wavelength is smaller; the speed of sound is constant; and frequency equals speed of sound divided by wavelength, so the frequency increases. There the formula itself is a marking point, and any rearrangement or symbols are allowed.
Redshift, the same idea on a cosmic scale
Light from distant galaxies is shifted towards the red, meaning longer wavelengths and lower frequencies, because those galaxies are moving away from us.
The further away a galaxy is, the greater its redshift, so the faster it is receding. That relationship is the evidence that the universe is expanding, and running it backwards is the argument for the Big Bang.
Strictly the wavelengths are stretched by the expansion of space itself rather than by the galaxy moving through space, but the observation and the reasoning are the same as for the siren.
Answering a Doppler question
Say what happens to the wavefronts, then to the wavelength, then to the frequency, then state that the wave speed is unchanged.
Four clauses, and they are usually four marks. If the question gives you an approaching source, every one of them is a decrease except the frequency, and it is worth writing the direction of each change explicitly rather than saying only that something changes.
Spec 3.1-3.8
What you need to know
- Compare transverse and longitudinal waves
- Use wave measurements and the wave equation correctly
- Explain wavefronts and the Doppler effect
Active recall
Quick check
Answer each question before opening the answer.
What is a wavefront?
A line joining points on a wave in the same phase
In a fixed medium, what happens to wavelength if frequency rises?
It decreases
What frequency change is heard from an approaching source?
The observed frequency increases
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