What of a wave is a measure of the energy it carries

The amplitude of a wave is a measure of the energy it carries. The amplitude of a wave is the distance between the midline of a wave and its crest or trough.

Amplitude measures the amount of energy being transported by a wave. The larger the amplitude, the more the energy that a wave has.

Wave such as water waves have energy. Smaller waves have less energy because they have a smaller amplitude. Tsunamis have very high amplitudes and thus have a huge amount of energy