"Looking at how the whip behaves gives a clue to this phenomenon (and it helps if you have actually tried to crack a whip). The whip has to be moved so that a U-shaped loop is formed near the handle, where the whip is thickest and stiffest. As the whip is swung, the loop travels outward toward the thinner, lighter tip. The loop travels progressively faster the closer it gets to the tip, because the energy from the heavier part of the whip is carried along into the lighter, thinner part. This amplification is analogous to way in which an ocean wave of small height becomes a high breaker as it enters the shallow water near the shore or over a reef.
"When the loop reaches the end, it is going extremely fast and causes the very tip to 'whip' around in a tight circle. It is at this point that the tip exceeds the speed necessary to create a tiny shock wave in the air; it is this shock that we hear as the 'crack.'