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Nodes and Antinodes

  1. May 21, 2009 #1
    1. The problem statement, all variables and given/known data
    Consider the standing wave: 0.005sin(30x)cos(420t) m. Locate the antinode closest to x=0.25 m.

    2. Relevant equations



    3. The attempt at a solution
    I'm not really sure how to tackle this problem except that i know that antinodes occur at the crests of the standing wave and that the distance between antinodes is lamda/2. In the answers it says that: kXn=(2n+1)pi/2..... Xn=(2n+1)pi/(2k) and when you plug in n=2 it is 0.261 m...does anyone know how they got the initial formula?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. May 22, 2009 #2

    Doc Al

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    Staff: Mentor

    Consider the spatial factor sin(kx). What values of x give the maximum amplitude?
     
  4. May 22, 2009 #3
    aren't they pi/2, 3pi/2, 5pi/2, 7pi/2...etc?
     
  5. May 22, 2009 #4

    Doc Al

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    Staff: Mentor

    Good. But that's the value for kx, not x. (In this problem, k = 30.) How would you write that series using n, where n = 0, 1, 2, and so on? Compare that to the formula given.
     
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