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What is the x>0 mean here? standing wave equation find nodes?

  1. Jun 11, 2013 #1
    1. The problem statement, all variables and given/known data
    Two waves travel in opposite direction form a standing wave of y= 2sin(31.42x)cos(7854t).
    Find the positions of first two nodes with x>0.


    2. Relevant equations



    3. The attempt at a solution
    The question didn't say whether the standing wave starts from node or antinode . The question didn't say how long is x, even I know the wavelength and frequency also don't know how to calculate, how? Please help
     
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  3. Jun 11, 2013 #2

    Dick

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    Tell me what 'node' means.
     
  4. Jun 12, 2013 #3
    The point that is not moving in standing wave. X=0. Then t= 0 ,then I will get first node, the second node, t=2?

    Thanks
     
  5. Jun 12, 2013 #4

    Dick

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    No, a node is a point where y=0 for all values of t. Try to find the first two value of x that satisfy 2sin(31.42x)=0.
     
  6. Jun 12, 2013 #5
    Yup, y=0, thank you very much
     
  7. Jun 13, 2013 #6
    Then for antinode position is dy/dT= 0 ? The amplitude is maximum for all kind of y.
     
  8. Jun 13, 2013 #7
    The position of the first two antinode s with x< 0. X<0 here mean they want the x value be negative , if I use, dy/dt = 0, then I will get sin34.42x= 0 , how to make x become less than zero here? Please thanks
     
  9. Jun 13, 2013 #8

    Dick

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    Antinode is where the amplitude reaches a maximum as a function of x. To find maxima you want to use calculus and solve dy/dx=0.
     
  10. Jun 13, 2013 #9
    Why I can't use dy/dT=0? Is that because x<0? What does that mean ? please .
     
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