Describing the Motion of a String at the Antinodes

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Homework Help Overview

The discussion revolves around the motion of a string at two adjacent antinodes within the context of standing waves. Participants explore the nature of motion at these points and how they relate to each other in terms of phase differences.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants question whether the antinodes are moving and if they move in phase or out of phase. There are suggestions to visualize the problem through sketches and to consider the implications of phase differences between adjacent antinodes.

Discussion Status

The discussion is active, with participants providing insights and asking clarifying questions. Some have attempted to interpret the motion and phase relationships, while others are exploring the implications of their sketches and the definitions of phase in relation to the motion of the string.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the information they can use or the assumptions they can make about the system being analyzed.

thatguy4000
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Homework Statement


How would you describe the motion of a string at two adjacent antinodes?

Homework Equations


N/A

The Attempt at a Solution


So would the antinodes not be moving since it's a standing wave? Or would they be moving in phase because they are propagating together?
 
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I suggest making a little sketch of what it looks like.
Can you imagine a snapshot of the string?
 
So this is what I have, the two ends of the "string" are clamped. When the wave is in action, the antinode will move up and down. But the question asks about the motion relating two adjacent antinodes. Does that mean the antinodes are not moving?
 

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thatguy4000 said:
But the question asks about the motion relating two adjacent antinodes
So mark an adjacent antinode, showing where it will be at the same time as the antinode position that you marked.
Where will each be a half period later?
 
Also, study the figure that you posted in #3. If you look at two adjacent antinodes, one is on the solid line and one on the dashed line. How do you interpret this?
 
haruspex said:
So mark an adjacent antinode, showing where it will be at the same time as the antinode position that you marked.
Where will each be a half period later?
One antinode point would be up and one would be down. Would that mean they are in phase though?
 
kuruman said:
Also, study the figure that you posted in #3. If you look at two adjacent antinodes, one is on the solid line and one on the dashed line. How do you interpret this?
The solid line is where the string is physically. The dashed line is where the string will be in half a cycle. How does this relate to phase?
 
thatguy4000 said:
The solid line is where the string is physically. The dashed line is where the string will be in half a cycle. How does this relate to phase?
That's what phase is - the fraction of a cycle difference in being at a given stage, where a whole cycle is a 2π phase difference.
 
Ok, that's what I thought. So then I answered they're moving with pi/2 phase difference but I got it wrong. The other options are not moving, moving in phase, and moving out of phase.
 
  • #10
thatguy4000 said:
Ok, that's what I thought. So then I answered they're moving with pi/2 phase difference but I got it wrong. The other options are not moving, moving in phase, and moving out of phase.
If 2π is one cycle, what is half a cycle?
 
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  • #11
Oh my gawd. I'm so dumb. Half a cycle is just pi so they're moving out of phase?
 
  • #12
thatguy4000 said:
Oh my gawd. I'm so dumb. Half a cycle is just pi so they're moving out of phase?
Yes. To the last statement.
 
  • #13
thatguy4000 said:
Oh my gawd. I'm so dumb. Half a cycle is just pi so they're moving out of phase?
Well done.
 

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