The increase in wave height as a tsunami approaches a coast is the result of the shortening of wavelengths.

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As a tsunami approaches a coast, its wavelength becomes shorter and the wave height increases. This is due to the fact that the front of the tsunami slows down as it enters shallower waters, while the back of the wave continues to move at the original speed. This causes the wave to "pile up", resulting in a higher wave height.

The Increase in Wave Height as a Tsunami Approaches a Coast