## Mastering Physics Solutions: Properties of Ocean Waves

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.

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?