This is the 2D top-down companion to the 3D "Doppler Effect" lab. Instead of drawing a formula-shaped ring pattern, this simulation literally records the source's position every time it emits a pulse and grows a real circle from that point at the true speed of sound, c = 343 m/s. The bunching ahead and spreading behind are a direct geometric consequence of the source moving between emissions — nothing about the spacing is computed from the Doppler formula.
Emit every T = 1/f_emit seconds at the source's CURRENT position
Each wavefront's radius(t) = c * (t - t_emitted)
f_obs = f_source * c / (c - v_radial)
v_radial = component of source velocity toward the observer
- Source speed sets how fast the source travels along its track, in real m/s, up to and past Mach 1 (343 m/s) — push it past the sound barrier to watch the wavefronts pile into a Mach cone, exactly the geometry that formula predicts as an emergent side-effect.
- Emission rate sets how often a wavefront is emitted (a low, visible rate stands in for an inaudible source frequency so the rings stay legible on screen — the physics and the Doppler ratio are identical at any frequency).
- Observer can be dragged anywhere, not just directly ahead or behind. The readout uses the general instantaneous Doppler formula with v_radial = the source's velocity component along the line connecting it to the observer, so moving the observer to the side genuinely reduces the shift toward 1.00×, and it correctly flips sign the instant the source crosses the observer's position.
- Enable the tone to hear an oscillator whose frequency is scaled by the same c/(c − v_radial) ratio the readout shows — the pitch shift you hear matches the number on screen.
Real-world relevance: this is the same physics behind a passing ambulance siren, police/weather radar speed measurement, and the redshift astronomers use to measure how fast galaxies recede.