The Doppler Effect

You’ve heard the Doppler effect thousands of times without knowing the name. An ambulance siren sounds higher-pitched as it races toward you, then suddenly drops to a lower pitch the instant it passes. A car horn sounds higher as it approaches, lower as it pulls away. A train whistle does the same thing.

The siren itself is playing the same note the whole time. The sound didn’t change. What changed is how those sound waves arrive at your ear — and that depends on the relative motion between you and the source.

The Core Concept

When a sound source moves toward you, it “chases” its own waves, scrunching them together. The wavelengths in front of the source are shorter — meaning higher frequency. Behind the source, waves get stretched apart — longer wavelength, lower frequency.

The same effect happens if you (the observer) move toward or away from a stationary source. Moving toward the source, you intercept wave crests more often (higher perceived frequency). Moving away, the crests take longer to catch up to you (lower perceived frequency).

Test your prediction with the simulation below. Set a source speed, press Play, and watch the wavefronts bunch together ahead of the moving source and spread apart behind it. Keep an eye on the observed frequency readout as the source passes the observer: it holds one steady value, then jumps.

The Doppler Equation

Rather than memorizing sign rules from scratch, use the SASH mnemonic and a sanity check.

How to Use the Formula

The key to getting the signs right: the perceived frequency should increase when source and observer are approaching, and decrease when they’re moving apart.

• Observer moving toward source: $f' = f(v + v_o)/v$ (more crests per second).
• Observer moving away from source: $f' = f(v - v_o)/v$.
• Source moving toward observer: $f' = fv/(v - v_s)$ (compressed wavelengths in front).
• Source moving away from observer: $f' = fv/(v + v_s)$.
• Both moving: combine the appropriate signs.

After plugging in: check whether $f' > f$ for approaching motion (or $f' < f$ for receding). If your answer goes the wrong way, you flipped a sign.

Worked Example

An ambulance siren emits a 700 Hz tone. The ambulance moves toward a stationary observer at 30 m/s. Speed of sound = 340 m/s. What frequency does the observer hear?

• Source approaching, observer stationary: $f' = fv/(v - v_s)$.
• $f' = 700 \times 340/(340 - 30) = 700 \times 340/310 \approx 768$ Hz.

The observer hears a higher pitch (768 > 700) — consistent with the source approaching. Once the ambulance passes and starts moving away, the formula flips to $f' = fv/(v + v_s) = 700 \times 340/370 \approx 643$ Hz. That sudden drop from ~768 Hz to ~643 Hz is exactly the “weeooooowwwww” you hear as a siren passes.

Doppler Effect for Light