Final answer:
The statement is true because energy is inversely proportional to wavelength; shorter wavelengths correspond to higher energy.
Step-by-step explanation:
The statement that 'The shorter a wave's wavelength, the greater its energy' is true. The energy of a wave is directly proportional to its frequency and inversely proportional to its wavelength. This means that as the wavelength decreases (shorter wavelength), the frequency increases, and so does the energy of the wave.
For electromagnetic radiation, such as light, this relationship can be visualized by imagining the effort required to produce short, tight waves in a heavy rope compared to long, wide waves. It takes significantly more energy to produce the shorter waves, which is analogous to how electromagnetic waves with shorter wavelengths carry more energy.