The Doppler Effect

Lesson 9 of 10 · 7 min · Free, no account needed

What you will learn

A moving source squeezes its crests together in front and spreads them out behind: the Doppler effect.
Coming towards you, a sound is higher; going away, lower. In still air: heard f = f × v ÷ (v − u) ahead.
The driver moves with the siren and hears no change. Radar guns and astronomers use the same shift.

An ambulance siren drops in pitch exactly as it passes you. Does the driver hear that drop too?
Move the siren. What happens to its crests?
Now listen. An ambulance drives past you.
The Doppler effect.
The Doppler effect: a moving source sends crests closer together ahead of it and further apart behind it.
Closer crests reach you more often: a higher frequency. Coming straight at you at speed u: heard f = f × v ÷ (v − u); going away: f × v ÷ (v + u).
It works for light too: stars coming towards us look a little bluer, stars moving away a little redder.
Simplified: still air, a source that moves straight towards or away from you, slower than sound.
How fast must a car go for its horn to sound 10 % higher in front?
Heard f ÷ f = v ÷ (v − u). For 1.10 you need v − u = 343 ÷ 1.10 = 312, so u ≈ 31 m/s.
Game: Speed gun. Catch the cars going over 60 km/h by their horn's pitch.
Every horn plays 400 Hz. Listen, or read the note.
Space: starlight has dark lines at known places. Which star is coming towards us?
A star moving towards us squeezes its light waves just like a siren squeezes sound: shorter wavelengths, so every dark line moves towards the violet end.
This siren is moving left. Put its last three crests in the right places.
A crest spreads out from the point where it was sent, not from where the siren is now. The siren moved left since then, so older crests are centred further right.
Back to the bet: hear the siren as the driver, then as you.

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