The figures show the vertical motion of a particle in water as a wave moves by. Suppose 16 inch waves occur every 6 s. What equation models the height of the particle as it moves from crest to crest?
Will post picture of the diagram in comments.

Question

The figures show the vertical motion of a particle in water as a wave moves by. Suppose 16 inch waves occur every 6 s. What equation models the height of the particle as it moves from crest to crest?
Will post picture of the diagram in comments.

anonymous · Answer

attachment

ranga · Answer

Amplitude = 16 inches
Time Period = 6 seconds
h = Asin(Bt)  or  A cos(Bt)
where A is the amplitude and period = 2*pi/B

ranga · Answer

For crest to crest I would probably go with the cosine function.

anonymous · Answer

I keep just going round and round on paper with this and not getting anywhere trying to solve the cosine function. My calculator keeps saying syntax error. :/

ranga · Answer

No calculator necessary.  Do you have answer choices?

anonymous · Answer

No I don't. It gives me the problem and the diagrams, and another students work. I need to identify and state the error and then completely redo the problem correctly.

anonymous · Answer

This is the work I have to find an error in.

ranga · Answer

h = A cos(Bt)
Amplitude A = 16 inches
Period = 6 seconds = 2*pi/B.  Therefore, B = 2*pi/6 = pi/3
h = 16*cos(pi/3 * t)

I am assuming in the diagram, the particle rises up by 16 in (top of crest) and goes to the bottom of the trough by 16 inches too.  So I am taking the amplitude as 16.  Not 100% sure if that is what is meant in the diagram.