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Standing Waves Equation

  1. Mar 18, 2009 #1
    1. The problem statement, all variables and given/known data

    Hi everyone. I am working on a physics research paper on Standing Wave Patterns and the physics of a viola. I found this formula for standing wave patterns and am having trouble making sense of it. When I tried, I got sin(0) which is 0 making the whole thing 0. Is this a valid equation and am I missing something?

    w = 2764
    t = (1/440)

    k = 2pi/wavelength
    x = distance traveled.

    I am sorry, but I am really confuesed

    2. Relevant equations

    y = 2yocos(wt)sin(Kx)



    3. The attempt at a solution

    2yo (2764)(1/440) = 2p1
    cos 2 pi = 1
    sin (0) = 0

    = Ahh!

    I may be using the variables wrong, but I used 2pi * frequency to get w, 1/frequency to get t
     
  2. jcsd
  3. Mar 18, 2009 #2
    y(x,t) = 2yocos(wt)sin(Kx) is the function which is dependent on both time and position. t is not the period.

    It's perfectly reasonable to get 0 a nodal points.
     
  4. Mar 18, 2009 #3

    Delphi51

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    Homework Helper

    I don't know the formula y = 2yocos(wt)sin(Kx) so perhaps I shouldn't be offering any help.
    But it seems clear to me that the sin(kx) = 0 at x = 0 is just telling you that there is no vertical movement of the string at x = 0. That would be the position where the string is attached. It seems a very reasonable result!
     
  5. Mar 18, 2009 #4
    Okay. Thanks.

    Excuse my ignorance, we had to research a topic that we haven't covered, but would it be more appropriate to use x as the string length, since that is further from where the string is attached and would cause vertical movement? I am not really understanding what I proved by getting 0...well I don't really understand what I am proving anyway.
     
  6. Mar 18, 2009 #5
    The equation you listed is modeling a string in two dimensions that is time dependent. So you can think of the function giving you the height of the string at some distance x, and some time t.

    x and t are variables that change.

    You proved that when sin(kx) = 0 then the height of the string is also 0. This makes sense since at x=0 there is a node.
     
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