Nearing the beach

Shallower means slower

Now we look at a real-looking beach, where the seabed slowly rises. The red dot out in deep water on the left draws a circle, while the dot near the beach draws a flat oval. The yellow crest markers also slow down as they get closer to the beach. A wave moving at 55 km/h in water 60 m deep slows to 21 km/h where the water is 3.8 m deep.

Why?People often say the wave “drags on the sand and brakes”, but that is only a small part of it. Waves slow down in shallow water mostly because of the depth itself. The shallower the water, the slower a rise and fall can pass along.

Learn moreIn very shallow water, wave speed is the square root of gravity × depth, so depth alone decides it. In water 3.8 m deep, that is about 6.1 m per second. The seabed on screen is drawn steeper than a real beach (a rough sketch).

Speed just before breaking

21 km/h

60 m deep

55 km/h

3.8 m deep

21 km/h

calculated from the textbook equations for water waves (linear wave theory)