Describing the Motion of a String at the Antinodes

In summary: You have successfully completed the summary.In summary, the motion of a string at two adjacent antinodes is out of phase.
  • #1
thatguy4000
8
0

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?
 
Physics news on Phys.org
  • #2
I suggest making a little sketch of what it looks like.
Can you imagine a snapshot of the string?
 
  • #3
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?
 

Attachments

  • Wave.png
    Wave.png
    4.6 KB · Views: 314
  • #4
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?
 
  • #5
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?
 
  • #6
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?
 
  • #7
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?
 
  • #8
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.
 
  • #9
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?
 
  • Like
Likes thatguy4000
  • #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.
 

1. What is the Antinode of a string?

The Antinode of a string is the point of maximum amplitude in a standing wave. It is located at the midpoint of the string and is where the string oscillates with the greatest displacement.

2. How is the motion of the string at the Antinode described?

The motion of the string at the Antinode is described as a point of maximum displacement and minimum velocity. The string is at its maximum amplitude and does not move up or down, but rather vibrates back and forth.

3. What factors affect the motion of the string at the Antinode?

The motion of the string at the Antinode is affected by the tension, length, and mass of the string. The frequency of the wave and the properties of the medium through which the wave is traveling also play a role.

4. How is the motion of the string at the Antinode different from the motion at other points?

The motion of the string at the Antinode is different from the motion at other points because it is at its maximum amplitude and does not move in a specific direction. At other points, the string may have a minimum or zero amplitude and move in a specific direction.

5. What is the relationship between the motion of the string at the Antinode and the wavelength of the wave?

The motion of the string at the Antinode is directly related to the wavelength of the wave. The distance between two consecutive Antinodes is equal to half the wavelength of the wave. As the wavelength increases, the distance between Antinodes also increases, resulting in a larger amplitude at the Antinode.

Similar threads

  • Introductory Physics Homework Help
Replies
6
Views
4K
  • Introductory Physics Homework Help
Replies
10
Views
2K
  • Introductory Physics Homework Help
Replies
19
Views
319
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
5K
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
4K
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
7
Views
4K
  • Introductory Physics Homework Help
Replies
4
Views
4K
Back
Top