Water Wave Speed


Dear mcasco,

I would like to know how the depth or volume of water in a fixed container affects the speed of a water wave and why? Please could you give a full explanation as this question has been bugging me for ages.

Many thanx


I can give you the facts in plain English in one paragraph. The detailed explanation involves some really ugly mathematics.

Waves are characterized by the distance from one peak to the next (wavelength), the time between successive peaks at a single point in space (period ). The speed of a wave which is not distorted by its interaction with the walls of the container will be its wavelength divided by its period. Waves like this where the depth of water is at least half the wavelength are called deep water waves. Waves in water where the depth is less than 1/20 of the wavelength are shallow water waves. The speed of these waves is greatly influenced by the interaction with the bottom so that their speed is essentially proportional to depth. For waves in between deep and shallow water waves, the speed varies somewhat with depth but less than a direct proportion. The volume of the container only matters in that small containers have not only bottoms but sides to consider. As long as the container holds water enough that the sides are several depths apart we may neglect this complication.

For the ugly mathematics I suggest that you read ugly math.

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