Final answer:
The amplitude of a wave is half the total vertical distance from the trough to the peak. For a wave with a peak-to-trough height of 15m, the amplitude is 7.5m, since the water rises and falls 7.5m from the equilibrium position.
Step-by-step explanation:
When discussing waves, particularly ocean waves, most people imagine the movement of water up and down. The student's question regarding wave measurements involves key terms such as amplitude, wavelength, peak, and trough. It is crucial to understand these terms to analyze the properties of waves.
The amplitude of a wave is defined as the distance from the equilibrium position (the still water level) to the crest (the highest point) of the wave, or equivalently, to the trough (the lowest point) of the wave. Since waves fluctuate symmetrically around the equilibrium position, the amplitude is half of the total vertical distance from the trough to the peak.
In the given example, a wave on the ocean measures 15m in height from peak to trough and has a wavelength of 12m. To find the amplitude, we simply divide the total height by two: amplitude = height / 2. Therefore, the amplitude of the wave is 15m / 2, which equals 7.5m. This indicates that from the still water level to the peak, as well as from the still water level to the trough, the water moves 7.5m vertically.