Visualize wavefronts from moving sources. Adjust source speed and see frequency shift, Mach cones, and sonic booms.
Follow successive wavefronts as an emitting source moves through its propagation medium. Adjusting the source speed shows compressed fronts ahead, expanded fronts behind, and the transition from ordinary Doppler shift to a Mach cone and sonic boom. The common misreading is that closely packed fronts mean the source itself is emitting more frequently. The emission rate can remain constant; source motion changes the spacing between fronts and therefore the rate at which they reach a stationary observer.
Each wavefront begins at the source position where that crest was emitted, then expands at the wave speed while the source continues moving. Consequently, successive centers do not coincide. Fronts are closer together in the direction of motion and farther apart behind the source, representing shorter and longer observed wavelengths respectively.
When the source reaches the wave speed, forward disturbances accumulate instead of moving ahead of it. Above that speed, overlapping wavefronts have a common envelope: a Mach cone, shown in a two-dimensional view as a V shape. For Mach number M greater than 1, its half-angle satisfies sin(mu) = 1/M.
No, not necessarily. A source may emit crests at a constant rate in its own frame while its motion changes the distance between successive wavefronts. A stationary observer then encounters compressed fronts more often as the source approaches and expanded fronts less often after it passes.
No, not as a quantitative light-frequency calculator. The moving-source wavefront construction describes waves propagating through a medium and supports sound-speed concepts such as Mach cones and sonic booms. Light in vacuum requires the relativistic Doppler relation, which does not use a source speed relative to a propagation medium.
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