# A tsunami is traveling at 450 km/h when the ocean depth abruptly doubles. Its new speed is roughly what?Tsunamis are ocean waves generally produced when earthquakes suddenly displace the ocean...

A tsunami is traveling at 450 km/h when the ocean depth abruptly doubles. Its new speed is roughly what?

Tsunamis are ocean waves generally produced when earthquakes suddenly displace the ocean floor, and with it a huge volume of water. Unlike ordinary waves on the ocean surface, a tsunami involves the entire water column, from surface to bottom. To a tsunami, the ocean is shallow-and that makes tsunamis shallow-water waves, whose speed is , where is the water depth and the gravitational acceleration. Tsunamis can travel thousands of kilometers across an ocean to reach the shore with their initial energy nearly intact; when they do, they can cause massive damage and loss of life.

jeew-m | Certified Educator

I think here the relation between speed of wave(v),ocean depth(d) and gravitational accelaration(g) is roughly;

v = sqrt(d*g)

So at initial depth;

450 = sqrt(d*g)----(1)

When depth doubles;

v = sqrt(2d*g)------(2)

(2)/(1)

v/450 = sqrt(2d*g)/sqrt(d*g) =sqrt2

v  = sqrt2*450 = 636.396km/h

SO when the depth doubles speed will be 636.396 km/h roughly.