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Slinky wave problem?

  1. Jan 25, 2015 #1
    1. The problem statement, all variables and given/known data
    A slinky with natural length of 3.00 meters, mass of 0.750 kg, and spring constant 18.0 N/m is stretched out along a floor, each end held by a seated person. The final length is 8.2 m. One end is plucked sending a transverse pulse. Find the pulse's travel time there AND back.

    2. Relevant equations
    I've been stuck on this problem for hours. It is driving me insane. I don't understand how to find the speed if I don't know the amplitude. Is it the natural length of 3 meters? Even then I still get the wrong answer.

    3. The attempt at a solution
    I've tried finding the solution multiple ways but still don't get the right answer. One method was using k = Ftension/x (8.2 m). Then putting that into v=squared root of F/(mass/length). Then used the velocity = wavelength * frequency to solve for frequency, took the inverse and multiplied by two.
    PLEASE HELP! I've been working on this for hours! I'd really appreciate it.
     
    Last edited: Jan 25, 2015
  2. jcsd
  3. Jan 25, 2015 #2

    haruspex

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    What is that supposed to say?
    That looks right, except I'm not sure that 8.2m is the right length to be using. Depends on your answer to my first question.
     
  4. Jan 25, 2015 #3
    Oh sorry. It's supposed to say the final length is 8.2 meters. As in the slinky is stretched to 8.2 m.
    Sorry about that.
     
  5. Jan 25, 2015 #4

    haruspex

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    OK, so how are you calculating the tension?
     
  6. Jan 25, 2015 #5
    Well I have the spring constant and I have the distance it is stretched (8.2 m) so I do 18N/m = F/8.2m and solve for F. Is this not right? Or am I supposed to use the natural length instead?
     
  7. Jan 25, 2015 #6

    haruspex

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    That's not the distance it is stretched (by).
     
  8. Jan 25, 2015 #7
    Oh...crap. So I subtract the natural length of 3 m from that then use it to find the tension, right?
     
  9. Jan 25, 2015 #8

    haruspex

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    Yes. (But I think what you did gives the speed for ;longitudinal waves.)
     
  10. Jan 25, 2015 #9
    How would I find the speed of a transverse wave?
     
  11. Jan 25, 2015 #10

    haruspex

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    Sorry, I've confused you. I mean that using the extension (8.2-3) gives the transverse wave speed, but using the total length (as you did initially) gives the longitudinal speed.
     
  12. Jan 25, 2015 #11
    Oh okay. I finally got the right answer! Thank you so much I've been working on this since yesterday. Really appreciate it!
     
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