How to play Shallow Beach
- Choose a test and read the wavelength, the speeds, or the angles on the card.
- Use f₂ = f₁, λ₂ = λ₁·v₂ ÷ v₁, sin θ₁ ÷ sin θ₂ = v₁ ÷ v₂, and v = √(g·h).
- Type your prediction and press Start. Watch the crests cross the edge.
- Compare the orange path or marks with the white path and crests over the sandbank.
Refraction: waves that change speed
Refraction is the bending of a wave when it passes into a place where it travels at a different speed. Sea waves show it well. In shallow water their speed depends on the depth, v = √(g·h), so as they run onto a sandbank or towards a beach they slow down. The frequency is set by whatever made them and can't change at the edge, so the slower waves bunch up: λ₂ = λ₁·v₂ ÷ v₁. If a line of crests meets the edge at an angle, the end that arrives first slows first, and the whole line swings round towards the normal. The rule, Snell's law, links the angles to the speeds: sin θ₁ ÷ sin θ₂ = v₁ ÷ v₂. That is why waves almost always reach a beach nearly parallel to it, however they started out at sea, and why they wrap around headlands. Light bends the same way going into glass or water, and sound bends in air layers of different temperatures.
A focused learning model
The sea has two depths with a straight edge between them; waves are long and gentle, keep their height, and nothing reflects at the edge. Crests are drawn as lines where the phase is a whole number, worked out so that it is continuous across the edge. The side view shows the water along the waves' path and the seabed step, not to scale. Runs show three periods and are paced by the factor shown. Answers within 2% are right.