Water Wave Speed

## Question:

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

## Answer:

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.

This information is brought to you by M. Casco Associates, a company
dedicated to helping humankind reach the stars through understanding how the
universe works. My name is James D. Jones. If I can be of more help,
please let me know.

JDJ