Forces on a String with a Transverse Wave

AI Thread Summary
The discussion revolves around calculating the total force exerted by the rest of a rope on a section carrying a transverse wave described by the equation y = 0.06 cos(2.1 t - 3.8 x). The problem specifies analyzing a half-wavelength segment of the rope at zero displacement, while neglecting the weight of the rope. Participants note that the horizontal components of force cancel each other out, leaving only the vertical components to consider. The key challenge is determining how to calculate the vertical acceleration from the wave equation. Understanding the relationship between displacement and acceleration is crucial for solving the problem.
Thefox14
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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

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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Thefox14 said:
The transverse displacement of a harmonic wave on a stretched rope is y = 0.06 cos(2.1 t - 3.8 x)

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?
 

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