How Do You Calculate the Amplitude of Ocean Waves?

[sphouxay]

Homework Statement

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 3.00 second for the boat to travel from its highest point to its lowest, a total distance of 0.690 meter . The fisherman sees that the wave crests are spaced a horizontal distance of 6.50 meter apart.

What is the amplitude of each wave?

Homework Equations

The Attempt at a Solution

If the maximum displacement is .690 wouldn't that be my amplitude of each wave, just need total understanding on this since, i read in my text its the total displacement of the crest and the total displacements of the trough.

 

[cepheid]

Hi sphouxay, welcome to PF.

Please include units in all of your statements, otherwise they are meaningless.

The amplitude of a wave is indeed its maximum displacement from the equilibrium position in either direction. So, in this context, it is the height of a peak or the depth of a trough above or below the water's surface. Careful though. That is not quite the same as the "0.690" stated in the problem.

Mathematically if a wave is described by A*sin(phase), then A is the amplitude, and the disturbance will oscillate between +A and -A.

 

[sphouxay]

so are you saying the amplitude is 0.690/2, which is .345 meters

 

[cepheid]

Yes, that is what I am saying.

 

[Borek]

Boat doesn't move just up and down, it rather makes circles or ellipses (depending on the water depth, I believe these are circles when the depth is large enough to be treated as infinite). So the total distance is half of the circle, which means amplitude is smaller.

But I doubt question is that tricky.

See http://en.wikipedia.org/wiki/File:Wave_motion-i18n-mod.svg