Describing the Motion of a String at the Antinodes

[thatguy4000]

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?

 

[tech99]

I suggest making a little sketch of what it looks like.
Can you imagine a snapshot of the string?

 

[thatguy4000]

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?

 

[haruspex]

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?

 

[kuruman]

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?

 

[thatguy4000]

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?

 

[thatguy4000]

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?

 

[haruspex]

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.

 

[thatguy4000]

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.

 

[haruspex]

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?

 

[thatguy4000]

Oh my gawd. I'm so dumb. Half a cycle is just pi so they're moving out of phase?

 

[haruspex]

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.

 

[tech99]

Oh my gawd. I'm so dumb. Half a cycle is just pi so they're moving out of phase?

Well done.