the speed of a shallow-water wave is a function of the wavelength and/or the wave period

The speed of a shallow-water wave is indeed influenced by both the wavelength and the wave period. In shallow water, the speed of a wave depends primarily on the water depth.

1. Wavelength: The wavelength of a wave is the distance between two consecutive crests or troughs. In shallow water, where the depth is significantly less than the wavelength, the speed of the wave is directly proportional to the square root of the product of the gravitational acceleration (g) and the wavelength (λ). This relationship is described by the shallow-water wave equation.

2. Wave Period The wave period is the time it takes for one complete wave cycle to pass a fixed point. The speed of a wave can also be influenced by the wave period. In shallow water, longer wave periods (i.e., waves with lower frequencies) travel faster than shorter wave periods (waves with higher frequencies). This is because longer wave periods are associated with longer wavelengths, and in shallow water, longer wavelengths result in faster wave speeds.

So, both the wavelength and the wave period are factors that affect the speed of a shallow-water wave.