Doppler Shifts and Bow/Shock Waves

The following particles are emitting sound waves which travel at the same velocity in all directions (in a way, these animations can represent other types of waves too such as the water-wake from a boat or jet ski.... although, to try to compare this to siesmic waves would require a moving epicenter which doesn't quite happen in nature to my knowledge, and the comparison to moving charged particles emitting EM-fields could be made too, at least for non-relativistic velocities where the energy isn't being transferred into the mass of the particle). Anyhow....

(1) The particle at rest is emitting a wave that travels outward in all directions at a constant speed.




(2) This next particle is moving to the right at a speed which is less than the speed of sound (or the corresponding wave speed). This creates creates a bow wave whereby the frequency in front is greater than the frequency behind, and hence a doppler shift.


(3) This, the fastest particle, is traveling at the speed of sound, or Mach 1, which creates a shock wave or a shock-cone.


(4) Here is a shadowgraph of a scale model rocket-plane doing a pitch maneuver at Mach speeds in a wind tunnel, whereby the denser air at the high pressure wavefronts change the index of light refraction which shows up as blackened lines on the exposed film (courtessy NASA, I think).