How is amplitude related to the energy carried by a wave?

Amplitude is fundamentally linked to the energy carried by a wave. Specifically, in many types of waves, such as mechanical waves or electromagnetic waves, the energy transported is proportional to the square of the amplitude. This means that as the amplitude increases, the energy carried by the wave increases significantly. For example, doubling the amplitude of a wave results in four times the energy.

This relationship occurs because the amplitude represents the maximum displacement of particles from their equilibrium position in wave motion. Greater displacement means that when the wave propagates, more work is done on the medium, thereby transferring more energy. This correlation is crucial in understanding wave mechanics, particularly in contexts such as sound waves and seismic waves, where energy transfer is vital for analyzing wave behavior and effects.

The other options suggest a misunderstanding of this relationship, as they imply that higher amplitude either decreases energy or has no connection to it, which does not align with established wave physics principles.