Motion toward you packs the waves tighter, so the frequency rises
Here v is the speed of the wave in its medium (about 343 m/s for sound in air), vo is the observer's speed and vs the source's. The received frequency f′ goes up when the two are approaching and down when they separate. The tricky part is the signs, not the arithmetic.
Getting the signs right is the whole game
- Observer approaching. Add vo in the top — you sweep into the waves faster, so f′ rises.
- Source approaching. Subtract vs in the bottom — the source chases its own waves, crowding them, so f′ rises.
- Moving apart. Flip each sign: vo subtracts, vs adds, and f′ falls below the source frequency.
- Rule of thumb. If the gap is closing, the answer must be higher than f. If it is opening, lower. Check your result against that before trusting it.
Simplified cases when only one thing moves
| Situation | Formula | Result |
|---|---|---|
| Both at rest | f′ = f | no shift |
| Observer moving, source still | f′ = f × (v + vo) / v | higher if approaching |
| Source moving, observer still | f′ = f × v / (v + vs) | lower if receding |
Sound needs a medium, so these hold for air or water. Light travels through a vacuum and uses the relativistic version, f′ = f × √[(1 − β) / (1 + β)], where β = v/c.
Common questions
Why does an ambulance siren change pitch as it passes?
As it approaches, its sound waves get bunched up in front of it, so they reach you more often and the pitch sounds higher. Once it passes and moves away, the waves stretch out and the pitch drops. The siren itself never changes tone; only the frequency you receive does.
Does it matter whether the source or the observer is moving?
For sound, yes, slightly. A moving source changes the spacing of the waves it emits, while a moving observer changes how fast they sweep past. The two cases use different terms in the formula, so equal speeds do not give identical shifts.
What is the difference between redshift and blueshift?
Blueshift means the observed frequency rose because source and observer are closing in; the wave is compressed toward the blue end for light. Redshift is the opposite: they are separating, the wave stretches, and frequency falls.
