An ambulance screams towards you, passes, and races off. The siren drops in pitch the moment it goes by — you have heard it a hundred times. Here is the strange part: the siren never changed. It sang exactly one note the whole way. What changed was the spacing of the waves arriving at your ear, and it changed because the source was chasing its own sound.
📘 What you need to know
The Doppler effect is the change in observed frequency caused by relative motion between a source and an observer
The source frequency never changes. Nor does the wave speedv through the medium
Source moving towards you → wavelength shortened (λ − Δλ) → frequency increased
Source moving away from you → wavelength lengthened (λ + Δλ) → frequency decreased
Δλ is the change in wavelength — the bigger it is, the bigger the Doppler shift
It happens for all waves: sound and light
For light: moving away → red-shifted; moving towards → blue-shifted
Nobody moving: nothing happens
Start with a source sitting still, pumping out waves at a steady frequency. The wavefronts spread out as perfect circles, evenly spaced in every direction.
No relative motion, no Doppler effect. Left and right are identical.
Move the source, and the circles bunch up
Now let the source move to the right at speed us. Each wavefront still spreads out as a circle from wherever the source was when it emitted it — and by the time it emits the next one, the source has moved forwards.
Ahead of the source, the circles are crowded together. The wavelength there is λ − Δλ, and the observer hears a higher frequency
Behind the source, the circles are stretched apart. The wavelength there is λ + Δλ, and the observer hears a lower frequency
The circles never change size or speed. Only where they were born has moved
Look at the gaps along the line. Ahead of the source they are tight; behind, they are wide. Same waves, same speed — different spacing.
Picture a duck paddling across a pond, sending out ripples. The ripples don’t speed up just because the duck is swimming. The duck simply catches up a little with the ripple it made a moment ago, so the ones in front get packed together. That packing is the Doppler effect. Nothing more mysterious than that.
Why the frequency changes
The wave speed v is set by the medium, not by the source. Air doesn’t care how fast the ambulance is going — sound travels at about 340 m s−1 regardless. So look at the wave equation:
The whole argument in one linev = fλ with vfixedλ shrinks → f must rise • λ grows → f must fall
And the change in wavelength has a name:
Change in wavelengthΔλ = change in wavelength (m)bigger Δλ → bigger Doppler shift
Source moves towards you
wavefronts bunch up
λ shorter
v = fλ, v fixed
f higher higher pitch
The trap: the source’s own frequency is constant the entire time, and so is the speed of sound. Only the observed frequency changes. Write “the observed frequency increases”, never “the siren’s frequency increases”.
The moment it passes you
Here is something people get wrong. The pitch does not slide smoothly downwards the whole time the ambulance drives past. While it is approaching you hear one steady high note; while it is receding, one steady low note. The drop happens as it goes by.
The famous neeeee-owwww. Two near-constant notes with a rapid slide between them, not one long glide.
It works for light too
Nothing in the argument was about sound. Any wave will do, including light.
A source moving away has its light stretched to longer wavelengths — towards the red end of the spectrum. It is red-shifted
A source moving towards us has its light squashed to shorter wavelengths — towards the blue end. It is blue-shifted
This works because red light has a longer wavelength than blue light
Relative motion
Wavelength
Observed frequency
Sound
Light
Moving towards observer
Shorter (λ − Δλ)
Higher
Higher pitch
Blue-shifted
Moving away from observer
Longer (λ + Δλ)
Lower
Lower pitch
Red-shifted
No relative motion
Unchanged
Unchanged
Same pitch
No shift
Notice the table says relative motion. It genuinely does not matter who is moving. If you run towards a stationary siren, the wavelength sitting in the air is unchanged — but you sweep through more wavefronts every second, so the frequency you receive goes up anyway. Same effect, different bookkeeping.
🚑 Answering any Doppler question
Are they getting closer or further apart? That single question decides everything.
Closer → wavelength shorter, frequency higher (higher pitch, blue-shift).
Further → wavelength longer, frequency lower (lower pitch, red-shift).
Sanity check: the source frequency and the wave speed v never change. If your answer says they did, something has gone wrong.
WE 1
A siren emits sound of frequency 500 Hz. The speed of sound in air is 340 m s⁻¹. An observer measures the wavelength of the sound reaching them as 0.60 m. Determine the wavelength emitted by a stationary siren, the change in wavelength, and the frequency the observer hears. State whether the siren is approaching or receding.
Step 1 — the wavelength if nothing movesλ = v/f = 340/500λ = 0.68 mStep 2 — the change in wavelengthΔλ = 0.68 − 0.60 = 0.08 mStep 3 — the observed frequency, using v = fλ with v unchangedf′ = v/λ′ = 340/0.60f′ = 567 HzStep 4 — conclude
The wavelength is shortened, so the siren is approaching.
Notice v = 340 m s⁻¹ was used twice, unchanged. Only λ and the observed f moved.
WE 2
An ambulance drives along a straight road at constant speed, siren wailing, and passes a pedestrian standing on the pavement. Describe and explain what the pedestrian hears, and state what happens to the frequency emitted by the siren.
While it approaches
Wavefronts bunch up in front, so λ is shortened. Since v = fλ with v fixed, the frequency heard is higher than the siren’s — a steady high pitch.
As it passes
For that instant it is neither approaching nor receding, so the pedestrian hears the true siren frequency. The pitch drops sharply.
While it recedes
Wavefronts stretch out behind, λ is lengthened, so the frequency heard is lower — a steady low pitch.
The siren itselfunchanged throughoutThe siren’s frequency and the speed of sound are both constant. Only the observed frequency changes.
WE 3
A spectral line is measured in a laboratory at 656.3 nm. The same line, in light from a distant galaxy, is observed at 658.9 nm. Determine the change in wavelength, and state and explain whether the galaxy is moving towards or away from Earth.
Step 1 — the change in wavelengthΔλ = 658.9 − 656.3Δλ = 2.6 nmStep 2 — which way has it shifted?
The observed wavelength is longer, so the light has moved towards the red end of the spectrum.
Step 3 — conclude
Red-shifted, so the galaxy is moving away from EarthLonger wavelength means lower frequency means red. Same logic as the ambulance — just with light instead of sound.
💡 Top tips
Always say observed frequency. The source’s frequency is constant, and examiners are listening for that word.
The wave speed v is set by the medium and never changes. That is what lets you use v = fλ.
Closer together → shorter λ → higher f. Everything else follows from that one sentence.
Red = receding, and both words start with “re”. Blue = coming at you.
Sketching wavefronts? Draw the circles with staggered centres, not one shared centre.
⚠ Common mistakes
Writing that the source’s frequency changes — only the observed frequency does
Saying the sound waves speed up in front of the source. The wave speed is fixed by the air
Drawing the moving-source wavefronts as concentric circles — the centres must be staggered
Thinking the pitch slides down continuously the whole way past. It drops as the source passes
Muddling red-shift and blue-shift. Red light has the longer wavelength
Assuming only the source can move. It is the relative motion that matters
Quick recap: The Doppler effect is the change in observed frequency due to relative motion between source and observer. The wavefronts bunch up in front of a moving source (λ − Δλ, higher f) and stretch out behind it (λ + Δλ, lower f). The source frequency and the wave speed never change. For light, receding sources are red-shifted and approaching sources are blue-shifted.
So far this has all been in words and pictures. But if a star’s spectral line has shifted by 2.6 nm, exactly how fast is it running away from us? There is a beautifully simple equation for that, valid whenever the source is much slower than light. That’s the next page: the Doppler effect of light.
Doppler effect leaving you behind?
Book a free meeting and we’ll work through wavefront diagrams, red-shift and past-paper Doppler questions together.
