# Calculating Tsunami Velocities

We learned that it took about 15 minutes for the first tsunami waves to reach the shores of Northern Sumatra after the magnitude 9.2 earthquake that happened off the coast of Sumatra on December 24th, 2004. It created one of the most devastating tsunamis ever, killing 280,000 people and decimating coastal. So how fast do tsunamis travel?

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Tsunamis are what we call “barotropic gravity waves,” which means the entire water column is moving, and is driven by the acceleration due to gravity. Think of it like this: when you throw a ball up into the air, gravity acts upon it to pull it back toward the ground. Similarly, when a mass of water is pushed upward above a subduction zone, that water will be pulled back down due to gravity. But there is also an outward component, causing the water to move out in all directions, like seismic waves from an earthquake.

Here’s how we calculate how fast a tsunami will travel:

c =

where c = the speed of the tsunami, g = acceleration due to gravity (9.8 m/s2), and H is the height of the water column that is pushed up by the rebounding plate (in other words, the depth of water). To figure out how fast a tsunami will travel, one only needs to know the depth of the water in which the tsunami occurred, and plug this into the above equation as H.

Part 1. Imagine a tsunami occurs in the Pacific Ocean in water that is about 4,000 meters deep:

How fast will that tsunami travel? We must set up our equation c= . We simply plug in the value for acceleration due to gravity (g), which is a constant (see above), and the depth of the water (H). We multiply those values, then take the square root to get the velocity in m/s2. We always want to work in meters for H so it is consistent with the units of m/s2 we use for g.