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The question is: How far apart are two points whose displacements are 30 degrees apart in phase?

My own reasoning doesn't seem to agree with the solution I was provided.

Here is my thinking:

Phase = wt +/- kx

For the first point, let x = x1 and t = t.

For the second point, let x = x2 (and t = t)

So then the phase difference would be (wt-kx1) - (wt-kx2) = k(x2-x1).

Then, given v and f, lambda = v/f = 4 m, so k = 2pi/lambda = pi/2.

So phase difference, which is given to be 30 degrees, or pi/6 rad, becomes:

pi/6 = (pi/2)(x2-x1) -where solving for x2-x1 gives an answer of 1/3.

The solution I was given says that the phase difference = 2pi(x2-x1) = pi/6, which gives x2-x1 = 1/12.

I don't understand how the 2pi comes into it!

Could someone tell me where my thinking went wrong?