The Doppler Effect
Simple Explanation
The Doppler effect is the change in a wave's perceived frequency caused by relative motion between the source and the observer — a source approaching an observer sounds higher-pitched, and one moving away sounds lower-pitched.
Why Do We Need It?
The Doppler effect explains a genuinely universal wave phenomenon, from a passing ambulance siren's pitch shift to how astronomers measure whether distant stars and galaxies are moving toward or away from Earth using light.
See It
Three circles representing sound wavefronts, bunched tightly together on the right (ahead of the moving source) and spread farther apart on the left (behind it), with an arrow showing the direction of motion
Formula
The Doppler Effect
f' = f(v ± v₀) / (v ∓ v_s)
The frequency an observer hears shifts higher when the source and observer are approaching each other, and lower when they are moving apart, because relative motion changes how many wave crests reach the observer each second.
- f'
- — the frequency heard by the observer, in hertz (Hz)
- f
- — the frequency actually emitted by the source, in hertz (Hz)
- v
- — speed of sound in the medium, in metres per second (m/s)
- v₀
- — the observer's speed (+ if approaching the source, − if moving away), in metres per second (m/s)
- v_s
- — the source's speed (− if approaching the observer, + if moving away), in metres per second (m/s)
When to use it: Whenever the frequency heard by an observer needs to be found when a sound source and/or the observer are moving relative to each other.
Worked Example
Find the frequency heard from an approaching source
A source emits a sound at 500 Hz while moving toward a stationary listener at 20 m/s. Find the frequency the listener hears. (v=340 m/s)
Why Does This Work?
As the source moves toward the observer, each successive wave crest is emitted from a position slightly closer to the observer than the last — crowding the crests closer together in space, which the observer experiences as a shorter wavelength and therefore a higher frequency.
Real-Life Example
A passing ambulance siren's changing pitch
An ambulance siren sounds noticeably higher-pitched as it approaches, then suddenly drops to a lower pitch right after it passes by.
While approaching, the siren's sound waves compress ahead of it (higher perceived frequency); once past, they stretch out behind it (lower perceived frequency) — exactly the Doppler effect in action.
Practice
A stationary source emits sound at 400 Hz. An observer moves toward it at 17 m/s. Find the frequency the observer hears. (v=340 m/s)
HardCommon mistake
Mixing up the signs for an approaching versus a receding source or observer — approaching always raises the perceived frequency and receding always lowers it, but it is easy to apply the wrong sign in the formula by mistake.
Quick Review
- f' = f(v±v₀)/(v∓v_s).
- Approaching: higher perceived frequency. Receding: lower perceived frequency.
- Caused by wave crests crowding together or spreading apart due to relative motion.