What you are looking at
A source (say a siren) moves to the right, giving off a fresh
wavefront — a circular crest —
at a steady rate. Each crest then spreads outward at the wave speed v. Because the source keeps moving, every
new crest is emitted from a point a little further along, so the crests
bunch up ahead of the
source and
spread out behind it. The green observers hear the pitch that reaches them.
Why the pitch changes
Pitch is just how often crests arrive. Ahead of the source they are packed closer together, so they arrive
more often — a
higher frequency. Behind, they are stretched apart and arrive less often — a
lower frequency. For a source moving at speed v_s through a medium where waves travel at v:
f_ahead = f · v / (v − v_s) f_behind = f · v / (v + v_s)
This is the everyday siren effect: as an ambulance approaches you hear a raised pitch, and the instant it
passes and starts receding the pitch drops. The source itself never changes its note — only the geometry of
the arriving crests does.
Breaking the sound barrier
Turn the source speed up to
1 × v (Mach 1) and the source keeps pace with its own crests:
they all pile up on top of each other at the front into a single high-pressure
shock wave.
Push beyond it (supersonic, Mach > 1) and the source outruns its waves entirely, and the crests form a
trailing
Mach cone whose half-angle is set by the speed:
sin θ = v / v_s = 1 / Mach
When that cone sweeps over you, you hear the
sonic boom. Nothing reaches an observer ahead
of a supersonic source until the source has already passed — you see the jet before you hear it.
Things to try
Start slow and watch the gentle bunching; the pitch readouts show the split. Creep the speed toward 1 × v and
watch the front crests crush together into a shock. Cross into supersonic and see the Mach cone appear and
narrow as you go faster. The same effect on
light is the redshift and blueshift astronomers use to
measure how stars and galaxies move.