The Answer:

The "crack" occurs when the wave of motion traveling down a whip surpasses the speed of sound. The wave can move so quickly because a whip tapers from the handle to the tip. When a whip is snapped, the momentum from the motion at the handle is conserved, and consequently the speed increases as the diameter of the whip decreases. Thus the wave gathers speed as it continues down the length of the whip, and when its velocity exceeds the speed of sound it produces a small sonic boom—the distinctive "crack".

—The Editors