Energy and Amplitude

This means that a doubling of the amplitude of a wave is indicative of a quadrupling of the energy transported by the wave. A tripling of the amplitude of a wave is indicative of a nine-fold increase in the amount of energy transported by the wave. And a quadrupling of the amplitude of a wave is indicative of a 16-fold increase in the amount of energy transported by the wave. The table at the right further expresses this energy-amplitude relationship. Observe that whenever the amplitude increased by a given factor, the energy value is increased by the same factor squared. For example, changing the amplitude from 1 unit to 2 units represents a 2-fold increase in the amplitude and is accompanied by a 4-fold (22) increase in the energy; thus 2 units of energy becomes 4 times bigger - 8 units. As another example, changing the amplitude from 1 unit to 4 units represents a 4-fold increase in the amplitude and is accompanied by a 16-fold (42) increase in the energy; thus 2 units of energy becomes 16 times bigger - 32 units.