Waves on a String Fixed at the Ends

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Homework Help Overview

The discussion revolves around a problem involving waves on a string that is fixed at both ends. Participants are exploring how to represent the wave behavior graphically, particularly in relation to the concept of image waves and reflections at fixed boundaries.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants describe their graphical methods for constructing wave diagrams and question the use of image waves. There is a focus on how to accurately represent the wave behavior at the fixed endpoints and whether the approach taken aligns with the problem requirements.

Discussion Status

The discussion includes attempts to clarify the method used for constructing the wave diagrams, with some participants expressing uncertainty about their approaches. Guidance has been offered regarding alternative methods, but there is no explicit consensus on the correctness of the initial attempts.

Contextual Notes

Participants are working within the constraints of the problem statement, which specifies the use of an image wave and the behavior of waves at fixed ends. There is mention of a dotted line representing the image wave, which some participants are unsure how to incorporate into their solutions.

fjccommish
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Homework Statement
What will the wave look like after 3 seconds?
Relevant Equations
No equations - this is visual.
I tried drawing the wave, counting 3 meters (speed is 1 meter/s) and bounced back from the stationary point (at 5) when necessary.

Using this, I found the answer to be drawing 2.

Wondering if that's correct.

009.png
 
Last edited by a moderator:
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Welcome to PF!

Before indicating which drawing is the correct answer, could you describe in a little more detail how you constructed the diagram for your answer? The problem statement indicates that you are to make use of the "image wave" drawn with a dotted line in the second drawing of the problem statement. Did you use this image wave? If so, please describe how.
 
Yes, I did it graphically - took each point, moved it 3 units right or, if it hit 5, the number of units left that remained. When I had done all points, I added the waves (or subtracted, as the case may be.) I only focused on the left side, as the right would be a mirror image.



The video shows what I did.
 
Last edited:
fjccommish said:
Yes, I did it graphically - took each point, moved it 3 units right or, if it hit 5, the number of units left that remained. When I had done all points, I added the waves (or subtracted, as the case may be.) I only focused on the left side, as the right would be a mirror image.
I'm not following the part of your reply that I colored. Can you elaborate a bit? I'm still not clear regarding your use of the dotted image curve?
 
TSny said:
I'm not following the part of your reply that I colored. Can you elaborate a bit? I'm still not clear regarding your use of the dotted image curve?
I made a video to show what I did.



I didn't worry about the right side. I figured it would be a mirror image flipped, as shown in every answer choice.

I have no idea if I did it correctly.
 
Very nice. Your method is correct and choice 2 is correct.

However, there is another way to work the problem without worrying about "bouncing" or "reflecting" the wave back at the fixed point. This method makes use of the image wave. First, just move the actual wave 3 units to the right. Part of this wave will now extend beyond x = 5m. Second, move the image wave 3 units to the left. Part of this wave will now extend to the left of x = 5m. Finally, simply add these two waves together in the region x = 0 to x = 5. The result will agree with your method.
 
Thanks
 
fjccommish said:
Thanks
You are very welcome.
 

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