The Mathematics of Tidal Waves

How can 36 foot waves crash on the north shore of Hawaii each year?

While tourists watch these waves safely from the beach just 500 yards away.

In contrast a 6 foot tsunami wave the height of the wave shown below

Destroys an entire city within miles of the coastline.

This is the driving question that holds student interest while we learn about the properties of the Sine wave.

After learning about amplitude, wavelength, period and frequency we return to the Tsunami question.

SOLUTION

The power difference between these two waves can be best illustrated by looking at both waves from the side. The profile of the Hawaiian wave looks like this:

The wave appears to be 36 feet tall because it is 18 feet above the sea level and 18 feet below. The wave is only 350 feet long so the beach is only affected by the relatively small amount of water in blue.

Contrast this with the Tsunami wave below which has a wavelength of 300,000 feet or 60 miles. We've rescaled the graph to fit on the screen. The Tsunami wave is over 800 times longer than the Hawaiian wave above.

Although the wave is only 3 feet above sea level and 3 feet below, it contains 60 miles of water! This is why a wave with a height of only 3 feet can destroy a city within miles of the beach.