Final answer:
The energy in a wave is measured by its amplitude, which is the height of the wave from the center line to the peak or trough. Other properties such as frequency and wavelength, while important, do not directly define the wave's energy.
Step-by-step explanation:
The amount of energy in a wave is closely related to its amplitude, which is the vertical height from the center line to the crest (top) or trough (bottom) of a wave. While frequency, wavelength, and speed are important properties of waves, they are not the characteristics that directly measure a wave’s energy. When you increase the amplitude of a wave with a given frequency, the energy carried by that wave also increases. It's important to note that the speed of a wave is equal to the product of its wavelength and frequency, but it is not directly proportional to the energy of the wave.
For example, speaking more loudly results in sound waves with a higher amplitude, which is why loud sounds carry more energy and are perceived as louder. When comparing two waves with the same frequency and speed, the one with the greater amplitude carries more energy. Hence, amplitude is the correct answer to the question about the trait that measures the energy in a wave.