Doppler Effect Simulation | Fenwick Tutoring

Drag the green observer left or right along the track. Wavefronts are drawn as they are emitted; brighter rings are newer.

Time 0.0 s

Source speed u

Wave speed v

Source frequency f

Playback speed

Label the wavelength ahead of and behind the source

Mach number u/v =

Emitted by the source

Frequency

2.00

Wavelength

5.00

In front of the source

Wavelength

—

Frequency heard

—

Behind the source

Wavelength

—

Frequency heard

—

At the observer

Measured

—

Hz, from the gap between the last two wavefronts

Predicted

—

Moving source, stationary observer:
f′ = f · v / (v − u) approaching
f′ = f · v / (v + u) receding
λ′ = (v ∓ u) / f

The wavefronts all travel at the wave speed v. The source moves after emitting each one, so the rings are no longer concentric: they crowd together ahead and spread apart behind. The wave speed never changes; only the spacing does.

What to look for

Stationary source: concentric circles, equally spaced everywhere. The observer measures exactly the emitted frequency.
Slow source: each new ring is centred a little further along than the last. Ahead of the source the rings are squeezed to a shorter wavelength, so an observer there counts more wavefronts per second and hears a higher pitch. Behind, the opposite.
Source at the wave speed (Mach 1): every wavefront emitted so far has its leading edge at the source. They pile up into a single wall of wavefronts, the sound barrier.
Supersonic source: the source outruns its own waves. The rings form a V-shaped envelope, the shock cone, and an observer in front hears nothing until the cone sweeps past.
Check the formula: put the observer well ahead of the source and compare the measured and predicted frequencies. Then leave it where it is and let the source pass. The measured value drops from the approaching to the receding value.