Waves on water
Practical Activity for 14-16
Waves and ripples are sent along water in a long shallow trough. This could be one station in a circus of wave experiments.
Apparatus and Materials
- Plastic guttering, 2 m long, 100 mm wide
- End stop for guttering, 2
Health & Safety and Technical Notes
The guttering, both ends closed by end stops, rests on the bench. The sort of guttering that has a flat bottom needs no side supports to prevent it rolling over.
- Because waves of many sorts can be made, and they travel slowly, the device is good for observing how wave pulses superpose and pass through one another without being affected.
- Alternatively students could compare a measured pulse speed with a calculation based on theory.
Speed of long waves in deep water
g is the acceleration of gravity, for gravity is the force moving these waves along.
In deep water, surface tension forces, s, are too small to matter. The density, r, does not appear because if it rises, the force acting and the mass to be moved both increase by the same factor, with no net effect on the response time of water ahead of a wave front.
Speed of waves in shallow water
(λ >> h, amplitude << h)
h is simply the depth of the water.
In water whose depth is large compared to the wavelength, l, the wave speed expression contains two terms, one for gravity effects and one for surface tension effects. It is
where the symbols have the meaning given above.
For short wavelength (ripples), the second term predominates, and the speed is approximately
For long waves, the first term predominates, and the speed is approximately
Interested students may be referred to Tricker, Bores, breakers, waves and wakes or Barber, Water waves. Bores are a special case of shallow water waves v =
A bore can easily be made in the water trough by sweeping water along at a steady rate using a wide paddle.
Speed of tiny ripples on water
if wavelength is small.
These waves have a speed which depends also on the wavelength A. Surface tension forces move these waves along. There are gravitational forces on the tiny humps of water, but they are too small to matter.
This experiment has yet to undergo a health and safety check.