A whip tapers from a heavy handle to a hair-thin tip. When the hand snaps it, a wave loop runs along the whip carrying a fixed amount of kinetic energy. Because the mass of whip material under the loop shrinks the further it travels, the loop's speed must rise to keep that energy (and momentum) roughly conserved — the same trick a figure skater uses pulling in their arms:
v(s) = v_hand · A^s
s = 0..1 fraction of the way from handle (0) to tip (1)
v_hand = hand crack speed slider, m/s
A = taper energy-concentration factor slider
The tip speed v_hand · A can comfortably exceed the speed of sound in air (≈343 m/s). When it does, the tip itself briefly outruns the pressure wave it is pushing — a genuine miniature sonic boom, not just a loud snap. That's the real explanation for the whip's "crack": it has nothing to do with the material breaking or two ends colliding.
- Raise the hand speed — scales every point's velocity linearly, easiest way to cross Mach 1.
- Raise the taper factor — a thinner, more aggressively tapered tip concentrates energy harder, so the same hand speed produces a faster crack.
- Velocity-vs-position chart — shows the exponential speed-up along the whip and exactly where (if anywhere) it crosses the sound-speed line.
Real-world relevance: this is the same physics behind bullwhips, cattle whips and even the tapered braided ends of some ship's rigging — anywhere a flexible tapering line is snapped, energy concentration at the thin end can push local speed past what the surrounding medium can carry away smoothly.