Earthquakes, Tsunamis, Bullwhips
Waves carry energy. When the wave slows down, that energy is still in the wave, and it causes the amplitude to increase. (Note: when a wave slows down, its wavelength -- the spacing between adjacent crests -- decreases. So the energy per unit length is increased, and that goes into the amplitude.)
When a fault in the Earth suddenly releases energy, it creates a wave in the ground. When this wave reaches us, we call it an earthquake. The "epicenter" is the location at which the earthquake originated. It can be determined by noting when the earthquake wave arrived at several different locations -- just as the SOFAR system was used to located downed pilots in World War II.
If the earthquake wave reaches an area that has a slow wave speed, the amplitude is increased. This is what happened in downtown Oakland in the 1989 Loma Prieta quake. The earthquake wave passed right through much of Oakland without causing great damage, until it reached the area near the freeway. This region had once been part of the bay, and had been filled in. Such soft ground has a slow wave velocity, so the amplitude of the earthquake increased when it reaches this ground. The most dangerous areas in an earthquake are regions of landfill. The marina district in San Francisco was also landfill, and that is why it was so extensively damaged.
Earthquakes often trigger tsnamis, also known as "tidal waves". When these waves travel in the deep ocean, they have a very high velocity and a very long wavelength. They can travel right under a ship without anyone on board even noticing. But as they approach land, they are slowed down, so their amplitude rises. The rise can be enormous, and that is what causes the damage near the coast.
In a bullwhip, the thickness of the whip is tapered towards the end. When the whip is snapped, a wave begins to travel down the whip to the end. Because the end is thin, the velocity of the wave increases near the end. The loud "crack" that you hear from the bullwhip occurs when the velocity of the waves exceeds the speed of sound.
Note the difference. In earthquakes and tsunamis, the added danger comes because the wave enters a region in which it slows. In the bullwhip, the crack comes because the wave speeds up.
See the related Quake Page.