Final answer:
The speed of a shallow-water wave is proportional to the water depth, not amplitude, wavelength, or frequency. Amplitude represents the wave's energy, while speed in shallow water is influenced by depth.
Step-by-step explanation:
The speed of a shallow-water wave is proportional to the water depth. This phenomenon is explained by the fact that as the depth of the water increases, the speed of the wave increases as well. When examining wave properties, the speed (v) of a wave can be calculated by the product of its wavelength (λ) and frequency (f), given by the equation v = λ × f. This equation, however, does not include amplitude, which is a measure of a wave's energy rather than its speed. The amplitude of a wave is the vertical distance from the midpoint to the crest (or trough), and for a given wave, it remains constant irrespective of the wave's speed. Another important point to remember is that the wave's frequency is the wave speed divided by the wavelength, as given by f = v / λ. It's essential to understand that, unlike in deep water waves where speed is influenced by wavelength and frequency, in shallow-water waves, depth is the controlling factor for speed.