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Gre Problem # 85

  1. Aug 31, 2004 #1
    Another mind boggling problem,
    any effort will be relieving...

    here it is:
    Small-amplitude standing waves of wavelength lambda occur on a string with tension T, mass per unit length mue , and length L. One end of the string is fixed and the other end is attached to a ring of mass M that slides on a frictionless rod. When gravity is neglected, which of the following conditions correctly determines the wavelength? ( you might want to consider the limiting cases M->0 and M->infinity.
    (A) mue/M = (2pie/lambda)cot(2pie*L/lambda)
    (B) mue/M = (2pie/lambda)tan(2pie*L/lambda)
    (C) mue/M = (2pie/lambda)sin(2pie*L/lambda)
    (D) Lambda = 2L/n, n=1,2,3...
    (E) Lambda = 2L/(n+1/2), n=1,2,3...

    my confusion starts with neglecting gravity, what will the added ring do, if no gravity is present?
    to see the problem with a figure, please click on the link below, it is #85
  2. jcsd
  3. Sep 1, 2004 #2

    Tom Mattson

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    No, it isn't. I also tried searching for "standing waves", with zero instances found.
  4. Sep 1, 2004 #3
    Sorry Tom,
    that question was there couple months ago, it seems that they posted a new one now, I should have double checked before I posted it. but here is my attempted picture:

    *fixed end *wavy string *end attached to a ring that slides on a stick

    SOrry again, I was trying to draw it, but it was crooked when I posted it.
    I will try to search more for that test, to see if it is still somewhere online.
    THank you so much for your efforts.
    Last edited: Sep 1, 2004
  5. Sep 2, 2004 #4
  6. Sep 3, 2004 #5


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    About what confuses you... there is no gravitational force on M but it does provide inertia. Consider the limit [itex] M \rightarrow \infty [/itex], then teh possible wavelengths are [itex] \lambda = 2L, L, 2L/3....[/itex]. On the other hand, in the limit [itex] M \rightarrow 0[/itex], we have [itex] \lambda = 4L, 4L/3 ....[/itex] (fixed end/free end boundary conditions). using those limits, it's easy to pick the correct answer.

  7. Sep 3, 2004 #6
    Bingo Pat!
    thanks so much!! I just couldn't see it on my own :bugeye: ...
  8. Sep 3, 2004 #7


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    You're very welcome.

    It's always nice to get a thank you for answering a question :biggrin:
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