A tsunami of wavelength 215 km and velocity 550 km / h travels across the Pacific Ocean. As it a

step 1 Here we have given the wavelength which is equal to 215 km and the speed is given 550 km per hou

A tsunami of wavelength 215 km and velocity 550 km / h...

A tsunami of wavelength 215 $\mathrm{km}$ and velocity 550 $\mathrm{km} / \mathrm{h}$ travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)

Key Concepts

Wave Propagation

This concept involves understanding how energy and disturbances move through a medium. For tsunamis, the wave travels at a speed determined by the conditions of the ocean, such as depth, and by the intrinsic properties of the wave itself. This is key to calculating how long it takes for the wave to travel from one point to another.

Shallow Water Waves

Tsunamis are considered shallow water waves because their wavelengths are much larger than the depth of the ocean. This means that their speed remains approximately constant and is primarily determined by the water depth. This concept helps in understanding why tsunamis can cross entire ocean basins and why their behavior changes as they approach the coast.

Tsunami Warning Signs

One of the most critical warning signs of an approaching tsunami is the abnormal recession of water from the harbor and coastline. This happens when a trough of the tsunami arrives before the crest, and it offers a vital, though brief, period during which people can evacuate. Understanding this phenomenon is crucial for tsunami preparedness and response.

Wave Period

The period of a wave is the time it takes for one complete wavelength to pass a fixed point, calculated as the wavelength divided by the wave velocity. In tsunami contexts, knowing the period is important because the time interval between the departure of the trough and the arrival of the crest (often about half of the period) is the window for taking safety measures.

Time Calculation for Evacuation

This concept links the properties of the wave—its wavelength, speed, and period—to determine the available time for evacuation after the initial warning sign, such as the sea receding. Specifically, if the recession signals a trough, then roughly half the wave period (the time from trough to crest) represents the reaction time people have to get to safety.

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