How Long Does It Take for a Wave Point to Move Between Two Set Displacements?

[Matt H]

Homework Statement

If y(x, t) = (6.7 mm) sin(kx + (705 rad/s)t + ϕ) describes a wave traveling along a string, how much time does any given point on the string take to move between displacements y = -2.0 mm and y = +2.0 mm?

Homework Equations

I'm not sure where to start.

The Attempt at a Solution

That's the problem.

 

[Pyroadept]

Fix the value of x. Easiest value - take x = 0.

Then: y(0,t) = (6.7 mm) sin((705 rad/s)t)

Let y = -2 mm
Thus: 6.7sin(705t) = -2
Now solve for t.

Do the same for y = 2 mm

Subtract the two values (smaller from the larger) to find the time taken to go from one to the other.