What wave property gives a relative indication of the amount of energy a wave transmits?

Amplitude is indeed the wave property that provides a relative indication of the amount of energy a wave transmits. In wave mechanics, the energy carried by a wave is directly related to the square of its amplitude. This means that as the amplitude increases, the energy that the wave carries increases exponentially. For instance, in the case of sound waves, a wave with a larger amplitude is perceived as louder because it transmits more energy, while in light waves, a higher amplitude means a brighter light.

Understanding this relationship is fundamental when analyzing different types of waves, as it highlights the significance of amplitude in energy transmission across various contexts, whether in acoustics, optics, or other areas of physics. The other options—frequency, wavelength, and speed—play important roles as well, but they are more related to the characteristics of the wave itself rather than its energy transmission. For example, frequency is related to how often the wave oscillates in a given time period, and wavelength refers to the distance between successive crests or troughs in a wave; neither directly correlates with energy as amplitude does.