← Theory of RelativityPart 0 — Foundations · 04

Why a Siren Changes Pitch

▶ DRILL

Vika's siren races past. Its sound waves bunch up in front of her and stretch out behind — so George ahead hears a high EEEE↑ and Liza behind hears a low ewww↓, even though the siren itself never changed. That's the Doppler effect, and light plays the exact same trick with colourinstead of pitch — the groundwork for redshift later. Use the Explain it for a kid / a grown-upswitch to set the depth.

EXPLAIN IT FORsimple words, names & pictures
SIREN SPEEDfast
SLOW-MOnormal
Vika 🚨▶George♪ EEEE↑Liza♪ ewww↓
🧑 GEORGE — AHEAD
waves bunch up → higher pitch, EEEE↑
👧 LIZA — BEHIND
waves stretch out → lower pitch, ewww↓

The big idea — when something making a sound moves, its waves get squished in front and stretched behind. So a siren sounds high coming toward you and drops low as it passes — even though the siren never changed. Light does exactly the same trick, but with colour instead of pitch: bluer coming closer, redder moving away. That's how we know far-off galaxies are racing away — a drill for later. (And if the siren goes faster than sound, the waves pile into a wall — a sonic boom.)

# formulaf′ = f · c / (c ∓ v) — pitch up ahead of the source, down behind it (Doppler effect for sound)
# setupsiren speed in Mach (source speed ÷ sound speed) · listeners ahead and behind · past Mach 1 the crests pile into a sonic boom
# scalesound needs a medium, so source- and observer-motion differ slightly; light has none, so its Doppler shift is relativistic (the redshift drill)
# nextthe same effect with light explains why distant galaxies look red — coming in Part 2