How is amplitude defined in relation to a wave?

Amplitude in the context of a wave is defined as half the height of the wave from its equilibrium position to its peak (or trough). This means that amplitude specifically measures the maximum displacement of points on a wave from their rest position.

When considering wave properties, the amplitude is an indicator of the wave's energy; greater amplitude means more energy is carried by the wave. For instance, in sound waves, a higher amplitude correlates with louder sounds, while in light waves, it relates to brightness.

The other choices can help to understand why they don't define amplitude correctly. The full height of the wave encompasses both the positive and negative peaks, meaning it is twice the amplitude. The distance between two similar points of the wave represents the wavelength, not the amplitude. Lastly, the time taken to produce one wave refers to the wave's period, which is unrelated to the wave's amplitude. Thus, the definition of amplitude being half the height of the wave accurately captures its essence in wave physics.