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The Doppler effect: why a passing siren changes pitch

A speaker cart rolls past a microphone and sends out one pulse every instant. Each pulse spreads as its own circle from where the cart was. Watch the circles bunch up in front and stretch out behind, then press Pause and read the pitch ratio.

Emission point: where one pulse beganWavefront: a circle growing at the speed of soundHeard higherHeard lower

Speed Mach 0.50slowsubsonic only · below Mach 1

Pitch ratio at the observer

1.00440 Hz

Stationary observer · moving source

Straight on the line

Approaching 2.00

Receding 0.67

1/(1 − M) and 1/(1 + M)

Same source, different spacing

The source keeps one steady rhythm, and every circle is centred on where the cart was when it sent that pulse. Ahead, the cart nearly catches its own waves, so crests arrive close together. Behind, it runs away from them and they arrive further apart. The tape shows the same thing in time.

A teaching model

Waves are slowed and drawn flat on the floor; the speed of sound is c = 343 m/s, source tone 440 Hz, air still. Only the source moves, so f′ = f₀ · c / (c − v cosθ), with θ measured at the emission point. The cart turns around at the buffers. Sound is off until you switch it on.