Tsunami shows force of resonance in world


POSTED: Friday, March 05, 2010

The tsunami brought to mind the importance of resonance in physical processes and provides one more example of the unity of processes in the physical world. The physical world can be understood in terms of a few basic principles, and resonance is one of the most basic.

Resonance occurs when any oscillating system is driven at its natural period by an outside force. Many physical systems have a tendency to oscillate or vibrate, and when they do so there is a period of time that is characteristic of the oscillations, the resonant period.

One notable example is vibrating air molecules that transmit sound waves and resonate in the confined spaces of musical instruments and the human vocal tract. Another is vibrating atoms that absorb and emit light of different frequencies to create the colors of our world.

A body of water also has a resonant period. It is the amount of time it takes for water to slosh back and forth in its basin. For example, the period of the Atlantic Ocean is similar to a tidal day, resulting in a resonance that creates larger tides and different tidal patterns in the Atlantic than in the Pacific.

The shape and size of the container are major factors in the period—for example, the time it takes for the water to move from one side to another as in a bathtub or in a shallow pan in the kitchen. This time is one-half of the resonant period.

The physical model or analog for this is a pendulum, as with a child on a swing. It hangs straight down at equilibrium, analogous to the flat water in the tub. Adding energy by pushing the swing disturbs the equilibrium; the more energy, the greater the swing. Left alone the swing will eventually return to equilibrium as friction dissipates the energy of the initial push.

To cause a large oscillation of the swing with a single push requires a significant input of energy, a hard push. A series of light pushes over a large number of swings produces the same result, but only if the pushes are in sync with the swing's natural period.

Because tsunami waves are orders of magnitude longer than their heights, they manifest as rapid changes of water level that resemble the tides, but at much shorter intervals. They are waves, however, and behave like waves, interacting with the sea-floor topography.

In extreme cases where the offshore topography is shallow or steeply sloping, the tsunami wave might break, creating a disastrous moving wall of water. In milder cases, such as with last Saturday's tsunami, the water level at the shoreline rises and ebbs over a period of several minutes.

Both the outline and the sea floor of Hilo Bay are shaped perfectly to focus the energy of a tsunami as the waves enter the bay. But its resonant period is about 30 minutes. This tsunami had a period of about 20 minutes.