IGCSE Physics 0625: Refraction and Reflection of Waves in a Wave Pool

A water-sports training centre has a large wave pool used to train surfers. Paddle-generated swell waves start out in deep water at one end of the pool, then cross onto a gently sloping shelf where the water becomes much shallower, before some of the waves travel on to strike a solid vertical wall at the far end of the pool.

(a) State what happens to the speed of the swell waves as they cross from the deep water onto the shallow shelf, and use this, together with the idea of wavefronts, to explain why the waves change direction (refract) as they cross the boundary at an angle. [3]

(b) The frequency of the swell does not change as the waves cross from deep to shallow water. State what happens to the wavelength of the waves as their speed decreases, and explain why, referring to the equation $v = f\lambda$ . [2]

(c) Some of the swell waves travel on to strike the vertical wall and bounce back across the pool. State what happens to the wavelength and to the frequency of a wave when it reflects from the wall, compared with the wave arriving at the wall. [2]

Part (a): Why the waves change direction entering shallow water

Water waves travel more slowly in shallower water than in deep water. As a wavefront approaches the shelf at an angle, one end of the wavefront reaches the shallower water, and therefore slows down, before the rest of the wavefront, which is still travelling at the original (faster) speed in the deep water.

Because one part of the wavefront is now moving more slowly than the other part, the wavefront swings round, so the whole wave changes its direction of travel as it crosses the boundary. This change in direction, caused by a change in wave speed, is exactly what is meant by refraction.

Part (b): Effect on wavelength

The wave equation connects speed, frequency and wavelength:

$v = f\lambda$

The frequency of the swell is fixed by whatever is generating the waves (the paddle), so $f$ does not change as the wave crosses onto the shelf. Since $v$ decreases but $f$ stays the same, $\lambda$ must decrease in the same proportion as $v$ , so that the product $f\lambda$ still equals the new, smaller value of $v$ .

So the waves become more closely spaced (shorter wavelength) once they are in the shallower water.

Part (c): Reflection from the wall

When a wave reflects from a solid barrier such as the vertical wall, only its direction of travel reverses. The medium (the water) and the wave’s source frequency have not changed, so:

The wavelength of the reflected wave is the same as that of the incoming wave.
The frequency of the reflected wave is the same as that of the incoming wave.

Final answers

(a) Speed decreases in the shallow water; the near end of each wavefront slows first, swinging the wavefront round and changing the wave’s direction. This is refraction
(b) Wavelength decreases, because $v = f\lambda$ with $f$ constant means $\lambda$ must fall as $v$ falls
(c) Both wavelength and frequency are unchanged on reflection, only the direction of travel reverses