Tides are best described as which type of waves?

• A. Deep-water waves
• B. Standing waves
• C. Shallow-water waves
• D. Surface waves

Answer: (C)

Waves are classified by how the ocean depth compares to their wavelength. Tides have incredibly long wavelengths—spanning hundreds to thousands of kilometers—while the ocean is only a few kilometers deep on average. When the depth is small compared to the wavelength, the shallow-water approximation applies, and the wave behavior is that of shallow-water waves: gravity and depth set the wave speed (roughly c ≈ sqrt(g h)), and the motion is a surface gravity wave traveling across the ocean. That makes tides best described as shallow-water waves. They are not deep-water waves, since the water isn’t deep enough relative to the wavelength, nor standing waves, since tides propagate rather than form a fixed pattern. While they are surface waves, the most precise characterization in this context is shallow-water waves.