Physics · Waves & motion
An ambulance does not change the note of its siren as it races past you. Its motion changes how fast the sound waves reach your ear — and that is what you hear as the pitch dropping the instant it passes.
§1 · The idea
A sound's pitch is not a fixed property of the thing making it. It is the rate at which wave crests reach your ear. A higher rate sounds higher; a lower rate sounds lower. Hold that idea and the whole effect follows.
A still horn sends crests outward as evenly spaced rings, like ripples from a dropped stone. Every listener around it hears the same pitch. Now let the horn move. Between releasing one crest and the next, it travels a little way forward — so each new crest starts closer to the one ahead of it. Crests bunch up in front and spread out behind.
An ear in front now catches crests more often than before: a higher pitch. An ear behind catches them less often: a lower pitch. The horn's own note never changed. Only the spacing of the waves it leaves in the air did — and spacing is everything the ear measures.
§2 · See it happen
Drag the speed slider. The dot emits crests at a steady rate; watch them crowd ahead and stretch behind as it speeds up, and the arrival-rate readouts shift with them.
Takeaway: the faster the source moves, the harder it crowds its own waves ahead — pitch rises in front and falls behind, and the gap between the two widens with speed.
§3 · The math
One short equation turns a speed into a heard frequency. Sound travels at about 343 metres per second; v is the source's speed. Use minus while it approaches, plus while it recedes.
A siren sounds at a steady 700 Hz at the source. Set how fast it is moving:
Takeaway: the drop you hear is the jump from the approaching value to the receding one — the whole fall happens in the instant the source passes, not gradually.
§4 · Light does it too
Light is a wave, so the same rule applies: motion stretches or compresses it. For light, wave spacing is colour. A source moving away has its light stretched toward red; one moving closer is squeezed toward blue.
Each element absorbs light at fixed, known wavelengths, leaving dark lines in a star's spectrum. Astronomers measure how far those lines have slid from their lab positions. Drag a galaxy's speed below: the dashed marks are where the hydrogen lines belong at rest; the solid lines are where we observe them.
Takeaway: nearly every distant galaxy is redshifted — Edwin Hubble's 1929 reading that the more distant ones recede faster is the first direct evidence that the universe is expanding.
At the speeds shown, the simple wave picture (z ≈ v/c) is accurate. Near the speed of light the full relativistic formula is needed, and cosmological redshift is better described as the stretching of space itself than as motion through it — but the intuition is the same.
§5 · Check yourself