Forces on a String with a Transverse Wave

Thefox14

1. The problem statement, all variables and given/known data

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.



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.)

2. Relevant equations

[tex]v = \sqrt{\frac{Ften}{\mu}}[/tex]
[tex]\sum F_{net} = ma[/tex]

3. 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!

kjohnson

It seems like this equation would be a good place to start. If it's giving you the vertical displacement at any point 'x' at a given time then what would be the acceleration of that point?