This simulator animates a wave source moving across the screen while emitting circular wavefronts at a steady rate, and a stationary observer watching them arrive. Because the source keeps moving between each emission, the wavefronts bunch together ahead of the source and spread apart behind it — the geometric origin of the Doppler shift, computed live for both the approaching and receding cases.
• A moving source emitting expanding circular wavefronts at a steady rate set by its source frequency. • A stationary observer marker showing where wavefronts arrive, visibly closer together as the source approaches and farther apart after it passes. • Independently adjustable source speed, source frequency, and wave propagation speed. • Live readouts for the observed frequency during approach and during recession, computed from the standard Doppler relations.
The source emits wavefronts at a constant rate in its own frame, but because it is moving, each new wavefront starts from a slightly different position than the last. Ahead of the source, successive wavefronts are emitted closer together in space, so an observer in front of the source receives them more often — a higher observed frequency. Behind the source, wavefronts are emitted farther apart, so a trailing observer receives them less often — a lower observed frequency. Notice that the source's own frequency of emission never actually changes; what changes is how closely spaced the wavefronts become before reaching you.
The Doppler effect arises because a moving source emits successive wavefronts from different positions in space. This bunches wavefronts together ahead of the source (raising the observed frequency) and spreads them apart behind it (lowering the observed frequency), even though the source's own emission frequency never changes.
The observed frequency for an approaching source is f_observed = f_source × v_wave / (v_wave − v_source), where v_wave is the wave's propagation speed and v_source is the source's speed toward the observer.
The denominator in the approach formula (v_wave − v_source) goes to zero, making the observed frequency mathematically infinite — physically, this is the shock-wave condition where wavefronts pile up on top of each other, the same threshold behind a sonic boom.
It models an idealized point source moving in a straight line at constant speed with a stationary observer directly along that line — it does not include a moving observer, off-axis geometry, or medium-boundary effects.