# Forces on a String with a Transverse Wave

## Homework Statement

The transverse displacement of a harmonic wave on a stretched rope is y = 0.06 cos(2.1 t - 3.8 x), where x and y are in meters and t is in seconds. A 5 meter length of this rope has a mass of 1.5 kg.

[PLAIN]https://wug-s.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?cc/DuPage/phys2111/fall/homework/Ch-16-17-Waves/ec-tran-wave-forces/rope.GIF [Broken]

At time t = 0, consider a 1/2 wavelength long section of the rope which is carrying the wave between two points which have zero displacement (y = 0). What is the total force exerted by the rest of the rope on this section? (You may neglect any effects due to the weight of the rope.)

## Homework Equations

$$v = \sqrt{\frac{Ften}{\mu}}$$
$$\sum F_{net} = ma$$

## The Attempt at a Solution

I'm not sure how to approach this problem. So far what I have realized is that the X component of the force from the left half gets canceled out by the right half. So I really just need to find the Y component right? Though I'm not sure how to go about doing that.

Thanks!

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