Tsunamis are unlike wind-generated waves, which many of us may observed on a loc

Question

Tsunamis are unlike wind-generated waves, which many of us may observed on a local lake or at a coastal beach, in that they are characterized as shallow-water waves, with long periods and wave lengths. The wind-generated swell one sees at a California beach, for example, spawned by a storm out in the Pacific and rhythmically rolling in, one wave after another, might have a period of about 10 seconds and a wave length of 150 m. A tsunami, on the other hand, can have a wavelength in excess of 100 km and period on the order of one hour. As a result of their long wave lengths, tsunamis behave as shallow-water waves. A wave becomes a shallow-water wave when the ratio between the water depth and its wave length gets very small. Swallow-water waves move at a speed that is equal to the square root of the product of acceleration of gravity (9.8 m/s/s) and the water depth - let's see what this implies. In the Pacific Ocean, where the typical water depth is about 4000 m, a tsunami travels at about 200 m/s, or over 700 km/hr. Because the rate at which a wave loses its energy is inversely related to its wave length, tsunamis not only propagate at higher speeds, they can also travel great, transoceanic distances with limited energy losses. This animation (2.3 MB), produced by Professor Noboo Shuto of the Disaster Control Research Center, Tobabu University, Japan, shows the propagation of the earthquake generated 1960 Chilean tsunami across the Pacific. Note the vastness of the area across which the tsunami travels - Japan, which is over 17,000 km away from the tsunami's source off the count of Chile, lost 200 lives to this tsunami. Also note how the wave crests bend as the tsunami travels - this is called refraction. Wave refraction is caused by segments of the wave moving at different speeds as the water depth along the crest varies. Please note that the vertical scale has been exaggerated in this animation - tsunamis are only about a meter high at the most in the open ocean. (The Quick Time movie presented here was digitized from a video tape produced from the original computer-generated animation.)

Explanation / Answer

Tsunami's are shallow water waves, with long periods and wavelengths. The wavelength of the tsunami exceeds 100km and period on the order of one hour as compared to waves generated by winds. A wave is becomes shallow when the ratio of water depth and wave length gets very small. Shallow water waves move at the speed of square root of the product of the accleration of gravity and the water depth. Tsunamic waves travel at the rate of 200 m/s. Waves loses its energy inversely to the wave length, thus tsunami not only propogate at high spped, they can travel great distance. The Chilean earthquake caused tsumani waves to travel to about 17000 km and reached the coast of Japan. Tsumani waves crests bend as they travel due varing the spped at different segments of wave, this is known as refraction.

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