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Converting wavelengths involves changing units from one measurement system to another. In this exercise, the wavelength is initially given in nautical miles. Nautical miles are often used in navigation because they relate to the circumference of the Earth. Each nautical mile is approximately 1,852 meters. To convert the wavelength from nautical miles to meters, you multiply the number of nautical miles by 1,852.For instance, if the wavelength is 800 nautical miles, as in this exercise, it converts to meters by calculating:

• \[ 800 \text{ nm} \times 1852 \text{ m/nm} = 1,481,600 \text{ m} \]

This conversion is crucial for finding wave speed in meters per second later on. Converting accurately ensures that subsequent calculations are correct and the provided solution matches real-world measurements.

The wave period is the time it takes for two consecutive wave crests to pass a fixed point. It is essential for calculating wave speed. In the exercise, the wave period is given as 1 hour. To perform calculations in the metric system, which is based on meters and seconds, we must convert the hour-based period to seconds.There are 3,600 seconds in an hour, so you convert the period from hours to seconds like this:

• \[ 1 \text{ hour} \times 3600 \text{ s/hour} = 3600 \text{ s} \]

This conversion allows us to develop calculations that directly yield the wave speed in meters per second (m/s). Using seconds simplifies working with other converted measurements and keeps the calculations consistent.

The formula to calculate wave speed is fundamental. It relates the wavelength and the wave period in mathematical terms. The formula is:

• \[ \text{Speed} = \frac{\text{Wavelength}}{\text{Period}} \]

In our exercise:- The wavelength is 1,481,600 meters (after conversion from nautical miles).- The period is 3,600 seconds (after conversion from hours).Substituting these values into the wave speed formula gives:\[ \text{Speed} = \frac{1,481,600 \text{ m}}{3,600 \text{ s}} \approx 411.56 \text{ m/s} \]This equation's simplicity helps in understanding how different wave characteristics determine their speed. It traces directly from basic principles of motion, where speed is distance over time.

Understanding the impact of tsunami waves involves analyzing their speed and energy. The calculated speed of approximately 1,481 km/h illustrates the potential destructive power of these waves. Tsunamis travel at high speeds, allowing them to cover vast distances rapidly. Their large wavelength and speed enable them to carry immense energy, impacting coastal areas with devastating force. When tsunami waves arrive at shallower coastal waters, their speed decreases, but their height increases, leading to potentially catastrophic flooding. Key factors in tsunami impact include:

• Tsunami speed: High velocities mean they can reach coastlines quickly, offering limited warning time.
• Energy transfer: The vast energy sustained over long distances delivers a powerful impact upon reaching land.
• Wave height increase: As water depth lessens near shores, wave height amplifies, increasing potential destruction.

Analyzing these elements helps explain why these waves cause extensive damage and why understanding their characteristics is crucial for disaster preparedness.