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Distance to the nearest node along the back wall

  1. Jun 17, 2015 #1
    1. The problem statement, all variables and given/known data
    Two 512Hz tuning forks are placed 3.0 m apart on the bench at the front of a classroom. Each is 2.0 m from a side wall and the room is 7.0 m. The speed of sound is 343 m/s.
    b) If the back wall room is 10.0 m away what is the distance from the back corner of the room to the nearest node along the back wall?

    2. Relevant equations
    wavelength = speed/frequency
    Path length difference = (n-1/2)λ

    3. The attempt at a solution
    The wavelength of sound is found to be 0.67m (wavelength = 343 m/s / 512 Hz).
    path length difference = x - (3.5 - x) = 2x - 3.5 m
    2x - 3.5m = (n-1/2)λ
    x = [(n-1/2)λ + 3.5m]/2
    node = 1
    x = 1.92 m

    I have partial answers from my teacher. The central anti node is 3.5 m from the corner. The first node is 1.12 m from the central antinode. The second node is 3.35 m from the central anti node. The third node is 5.58 m (beyond the corner). The second node is 3.5 - 3.5 = 0.15 m from the corner. I do not understand how to find the distances of these nodes from the central anti node.
     
  2. jcsd
  3. Jun 17, 2015 #2

    andrevdh

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    This sounds (unintentional pun) like a double slit problem.
     
  4. Jun 17, 2015 #3

    haruspex

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    It's just geometry. Draw a diagram of the room. Mark an antinode, say, at distance x from the central antinode. How far is it from there to each fork?
     
  5. Jun 17, 2015 #4

    andrevdh

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    Node would be destructive interference.
     
  6. Jun 17, 2015 #5
    It does sound like a double slit problem.

    lodestar,

    I think it would help you to recall two things: why there is a node centered between the two forks and the wave equation.
     

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  7. Jun 17, 2015 #6
    Anti-node is destructive I believe.
     
  8. Jun 17, 2015 #7

    haruspex

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    No, andrevdh is right.
     
  9. Jun 18, 2015 #8

    andrevdh

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    tuning forks.jpg T1 and T2 are the two tuning forks.
    The path lenght difference between the two waves is the distance Δ in the drawing .
    Which is (n - 1/2)λ as you mentioned.
     
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