How Do You Solve an Oscillating Rope Problem?

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    Oscillating Rope
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The oscillating rope problem involves a rope under a tension of 120 N, fixed at both ends, displaying a second-harmonic standing wave pattern. The displacement equation provided allows for calculations of the rope's length, wave speed, mass, and period of oscillation in a third-harmonic pattern. Key points include identifying the number of nodes in the second harmonic, which are located at the ends and the midpoint of the rope. To solve the problem, plotting the displacement function can help visualize the nodes. Understanding these concepts is essential for approaching the calculations effectively.
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Homework Statement


A rope, under tension of 120 N and fixed at both ends, oscillates in a second-harmonic standing wave pattern. The displacement of the rope is given by
y = (1.18 m)sin ( x / 2) sin (10 t),
where x = 0 at one end of the rope, x is in meters, and t is in seconds.

(a) What is the length of the rope?

(b) What is the speed of the waves on the rope?

(c) What is the mass of the rope?

(d) If the rope oscillates in a third-harmonic standing wave pattern, what will be the period of oscillation?



Homework Equations


v=sqrt(t/density)
d=m/v


The Attempt at a Solution



I have no clue how to start this problem, can anyone provide a way to approach a problem like this?
 
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What does the second harmonic look like? Specifically, how many nodes are there and where are they located on the string?
 
the second harmonic has three nodes
 
Last edited:
Right, there are nodes at the ends of the string and one right in the middle. Now try plotting y vs. x and seeing where its zeros are. Those zeros correspond to the nodes on the string.
 

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