In physics, wave mechanics, and oscillatory systems, the total energy carried by a wave is directly proportional to the square of its amplitude. This fundamental mathematical relationship means that if you double the amplitude of a wave (such as a sound wave, light wave, or mechanical oscillation), the energy it transmits increases by a factor of four (22), while tripling the amplitude multiplies the energy output by a factor of nine (32), highlighting how even moderate increases in wave displacement require or release significantly greater amounts of energy.