Question

A fisherman notices that his boat is moving up and down periodically without any horizontal motion, owing to waves on the surface of the water. It takes a time of 2.30 s for the boat to travel from its highest point to its lowest, a total distance of 0.620 m . The fisherman sees that the wave crests are spaced a horizontal distance of 5.90 m apart.

How fast are the waves traveling?

Express the speed v in meters per second using three significant figures.

v=____________m/s

What is the amplitude A of each wave?

Express your answer in meters using three significant figures.

A= _____________ m

Answer 1

Time for wave to travel from highest point to lowest = 2.30 sec.
This corresponds to half of one wavelength.
Therefore, time for one whole wavelength = 4.60 sec.

The wave crests are spaced 5.90 m. apart.
This corresponds to the distance from one peak to the next peak of the waves.
By definition, this is one whole wavelength.
Hence, one wavelength = 5.90 m.

Since the speed of the wave = distance / time, we have speed = 5.90 m. divided by 4.60 sec.
And that is 1.2826 m / sec.; the speed of the wave in a horizontal direction.

As for the amplitude of the wave, the highest point of the wave to its lowest point is 0.620 m (The boat always sits on the wave - I assume it isn't sinking!)
This distance corresponds to the peak - peak vertical displacement of the wave.
Therefore, the amplitude is half of this, i.e. 0.31 m.