Waves on a String Fixed at the Ends

[fjccommish]

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.

 

[TSny]

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.

 

[fjccommish]

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.

 

[TSny]

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?

 

[fjccommish]

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.

 

[TSny]

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.

 

[fjccommish]

Thanks

 

[TSny]

Thanks

You are very welcome.