If y(x, t) = (4.7 mm)sin(kx + (675 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?

It takes 0.00127 seconds.

Explanation:

The equation its

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We want the time for ANY POINT, so, for convenience, lets take x=0

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Now, we want the positions

so, for the first position:

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and for the second one:

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Now, we can subtract both:

The strings take 0.00127 seconds.