A. The height of the wave
Wave amplitude refers to the maximum displacement of a particle on a wave from its equilibrium position. It is commonly represented by the height of the wave. It can be measured from either the equilibrium position to the crest (highest point) or from the equilibrium position to the trough (lowest point) of the wave.

B. The breadth of the wave
The breadth of a wave is not related to wave amplitude. The breadth of a wave refers to its width or the distance between two consecutive crests or troughs. It is a measure of the spatial extent of the wave, while amplitude is a measure of the magnitude of the wave.

C. Half of the wave height
Wave amplitude is not half of the wave height. The wave height refers to the vertical distance between the trough and the crest of the wave, while amplitude refers to the maximum displacement from the equilibrium position. The amplitude can be equal to, smaller than, or greater than half of the wave height, depending on the characteristics of the wave.

D. It is the time interval between two successive waves
Wave amplitude is not related to the time interval between two successive waves. The time interval between two successive waves is called the period or wavelength of the wave. Amplitude and wavelength are independent properties of a wave.

In conclusion, the correct answer is option A) The height of the wave. Wave amplitude is the maximum displacement of a particle on a wave from its equilibrium position, commonly represented by the height of the wave. It is not related to the breadth of the wave, half of the wave height, or the time interval between two successive waves.