Properties of Ocean Waves

Part A = 1.00 m/s

Part B = 0.350 m

Solution Below:

A fisherman notices that his boat is moving up and down periodically, owing to waves on the surface of the water. It takes a time of 2.80 s for the boat to travel from its highest point to its lowest, a total distance of 0.700 m. The fisherman sees that the wave crests are spaced a horizontal distance of 5.60 m apart.

Part A

How fast are the waves traveling?

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

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

It takes 2.80 s for the boat to go from peak to trough. Since the problem tells you that there are 5.60 m between *crests*, you take half that distance to tell you how far it is from peak to trough. That’s 2.80 m. So since it takes 2.80 s to go 2.80 m, you know the speed of the wave is 1.00 m/s. Don’t worry about the distance from the high to low point, that’s part of the amplitude, not the speed of the wave.

1.00 m/s

Part B

What is the amplitude A of each wave?

Express your answer in meters using three significant figures.

Express your answer in meters using three significant figures.

Similar to Part A, except you start with 0.700 m, the vertical distance between peak to trough. Since the amplitude is just from the *baseline* to the peak (or trough), divide by two. So the amplitude is 0.350 m.

0.350