# How is tsunami speed derived?

## Main Question or Discussion Point

I read that the speed of a tsunami is given by

c = sqrt(G * d)

where G is the gravitational constant 9.8 m/sec^2 and
d is ocean depth in meters.

How is this derived? I had always thought that wave speed was a constant depending only on the medium.

Also, is there some fundamental mechanical difference between a tsunami and a "normal" surface ocean wave?

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Do you also know the formula for the height of the wave. (Of course in respect to the clifs stepping.)

Hello lagrange,

The behaviour of tsunami is the behaviour of shallow-water waves.
Therefor the velocity of the waves is given by the equation for the shallow-water phase- and group velocity.

Here you'll find the linear theory of ocean surface waves:
http://oceanworld.tamu.edu/resources/ocng_textbook/chapter16/chapter16_01.htm

The shallow-water velocity equation (16.8) and (16.11) in this paper are derived using the equations (16.5)and (16.6).

More about ocean waves and tsunami:
http://oceanworld.tamu.edu/resources/ocng_textbook/chapter17/chapter17_02.htm