The best statement to describe who is correct is:
Brody is correct because the wave involves an input of energy.
When Brody waves his hand back and forth, he is indeed creating a disturbance that involves energy being transferred. This motion can be considered as a wave in a broader sense, even though it is not a mechanical wave like sound or water waves. Thus, Brody's assertion has merit in that it reflects the concept of energy input related to waves.