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Homework Help: Frequency of wave on a string

  1. May 8, 2006 #1

    kel

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    Hi

    I have a question that I'm not sure how to answer, it goes like this:

    A string along which waves can travel in 2.7m long and has a mass of 260g. The tension is 36N. What must the frequency of a travelling wave of amplitude 7.70mm be if the average power transmitted is 85W?

    I was going to use the average power question and worked out that the linear density would be 0.96 (or 9.6e-3), but I'm not sure how to go about finding the angular frequency or height of the wave (e.g. y) with the info given in the question or am I going about this in completely the wrong fashion?

    Also, where is the equation editor in this forum? I was going to write out the Power equ' but it would look fairly untidy in normal text.

    Thanks
     
  2. jcsd
  3. May 8, 2006 #2

    kel

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    Just realised the height (y) is the amplitude squared - which I work out to be:

    7.7mm = 7.7e-3 m, so that squared should be 5.929e-5, I think.

    If this is correct then I just need the velocity and angular wavelength.
     
  4. May 8, 2006 #3

    kel

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    ok, slight update. I have now worked out that the linear density is in fact 0.096 and the amplitude is 7.7e-3

    Could anyone tell me how I get the velocity from this? I mean the speed of the wave v
    (p=1/2*linear density*v*w^2*y^2)
    Thanks
     
    Last edited: May 8, 2006
  5. May 8, 2006 #4

    Hootenanny

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    The velocity on a wave can be obtained using the equation;

    [tex]v = \sqrt{\frac{T}{\frac{m}{L}}}[/tex]

    This can be derrived from the wave equation

    ~H
     
  6. May 8, 2006 #5

    kel

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    Thanks,
    I just realised that I can use the root of tension/linear density.

    and got a value of 19.36, does that sound about right?
     
  7. May 8, 2006 #6

    kel

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    Aha !!

    How does this sound?

    w^2= 85/0.5*(0.096)*19.36*(7.7e-3)^2
    w^2= 1542733.411
    w = root of the above = 1242 rad/s
    f = w/2pi = 197.67 Hz
     
  8. May 8, 2006 #7

    Hootenanny

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    I would agree with that.

    ~H
     
  9. May 8, 2006 #8

    kel

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    HOOOOORRRAYYYY!

    Hey are you any good with wave interference? My lecturer has been crafty and given us a question where I have 2 waves which interfere, but the only equation given is that of the resultant wave and I don't know how to resolve them back into their component waves.

    I know it's along the lines of vector algebra, but I'm clueless on this one I'm afraid.
     
  10. May 8, 2006 #9

    Hootenanny

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    I would also agree with that. Well done, you solved it without any help from me, I feel reducntant now :tongue2: . By the way, to insert mathematical equations see this thread; https://www.physicsforums.com/showthread.php?t=8997 . Also, if you click on any formulae in these forums a pop up will present the code used to produce the equation.

    ~H
     
  11. May 8, 2006 #10

    Hootenanny

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    If you post your question I guarantee someone on PF will be able to answer it :biggrin:

    ~H
     
  12. May 8, 2006 #11

    kel

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    Cheers! I'm sure I owe u a few beers by now tho!
     
  13. May 8, 2006 #12

    Hootenanny

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    Not a problem my friend :smile: . Damn, this virtual beer sure does taste good :cool:

    ~H
     
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