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Wave speed refers to how fast a wave propagates through a medium. To find the wave speed, you'll need to understand two important concepts: wavelength and period. The **wavelength** is the distance between consecutive wave crests, while the **period** is the time it takes for the wave to complete one full cycle.

To calculate the wave speed, use the formula:

• \( v = \frac{\text{wavelength}}{\text{period}} \)

In the example provided, the wavelength is 4.8 meters, and the wave's period is calculated by doubling the time from the crest to the trough, which totals 5 seconds.

Thus, the wave speed is:

• \( v = \frac{4.8 \, \text{m}}{5 \, \text{s}} = 0.96 \, \text{m/s} \)

Wave speed is essential in understanding how energy is transported across distances within a medium, like water or air.

Wave amplitude gives a measure of how tall or deep a wave is compared to its equilibrium (non-disturbed) position. It indicates the energy amount in the wave. The greater the amplitude, the more energy a wave carries. In any wave cycle, the amplitude is half the distance between the highest and lowest points of the wave.

You can calculate wave amplitude using this formula:

• \( A = \frac{\text{total vertical distance}}{2} \)

In the exercise, the boat moves a total vertical distance of 0.53 meters. Therefore, the amplitude is:

• \( A = \frac{0.53 \, \text{m}}{2} = 0.265 \, \text{m} \)

When the total vertical distance changes, like reducing to 0.30 meters, the amplitude adjusts accordingly to 0.15 meters. Knowing the amplitude helps predict the impact waves may have on objects in their path, crucial for things like boat stability.

The wave period represents the time it takes for a wave to complete one full cycle, measured in seconds. It's closely tied to frequency, where frequency represents how many cycles occur in a second. If you know how long one cycle takes (the period), you can determine the wave speed and vice-versa. Here’s how you find the period when given the time from crest to trough:

The given time from the boat's highest to lowest point is 2.5 seconds, meaning the half cycle period is known, and the full wave period is:

• \( T = 2 \times 2.5 = 5 \, \text{s} \)

Understanding the wave period helps in designing strategies for dealing with wave-related phenomena, such as predicting when a boat might stabilize after experiencing wave movements. This foundational concept not only applies to water waves but also to sound, light, and other types of wave motion we encounter.