Finding the total vertical distance - transverse wave

[PhysicsFriend]

Homework Statement

Suppose the amplitude and frequency of the transverse wave in the figure are, respectively, 5.89 cm and 5.00 Hz. Find the total vertical distance (in cm) through which the colored dot moves in 3.00 s.

http://i45.tinypic.com/3007ihy.png

Homework Equations

y = A sin (2pi x f x t - (2pi x)/λ)
v=λf
v= x/t

The Attempt at a Solution

x=vt
λ=v/f

x/λ = vt/ (v/f) = t x f = 15

Plug in x/λ = 15
Plug in A = .0589m
Plug in f = 5 Hz
Plug in t = 3.00 seconds

Answer = 0m

However, the online system says it is incorrect. I have no other strategy besides this one? Can someone help?

 

[voko]

You have found the displacement. Which is zero, because in 3.00 seconds the dot makes a few COMPLETE oscillations and returns where it was. You need to find the distance, which is the length of the total path the dot has gone through.

 

[PhysicsFriend]

OH
y = displacement and not distance! Got it.

Thanks so much!