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This is ! How do I solve the nodes and antinodes for this problem?

  1. Nov 20, 2012 #1
    HELP!! This is URGENT! How do I solve the nodes and antinodes for this problem??

    41.png

    For nodes, I tried doing λ = 2L/n but it's not giving me the answers they got... please help!!
     
    Last edited: Nov 20, 2012
  2. jcsd
  3. Nov 20, 2012 #2
    Re: This is URGENT! How do I solve the nodes and antinodes for this problem??

    Okay so check this diagram out
    http://www.physicsclassroom.com/mmedia/waves/h3.gif
    Thats a 3rd harmonic...
    So you've got 4 nodes where the string is not moving at all, and 3 antinodes of maximum displacement.
    Its fixed at each end, so 0m and 9m must be nodes! They cant move if there being held there. So youve got 2 in between , they must be equally spaced so theyve gotta be at 3m and 6m. (Maths way to do this is length/harmonic = 9/3 = 3, gotta be spaced 3m apart)
    You know that the antinodes must be halfway between these nodes, so they have to be at 1.5, 4.5 and 7.5! This is length/2*harmonic.

    For the frequency...
    velocity = root(tension/(mass/length))
    and then to get the frequency this must be divided by twice the length :)
    Hope you understood all that!!
     
  4. Nov 20, 2012 #3
    Re: This is URGENT! How do I solve the nodes and antinodes for this problem??

    sorry thats v = [itex]\sqrt{\frac{T}{M/L}}[/itex]

    so

    f = [itex]\frac{\sqrt{\frac{T}{M/L}}}{2L}[/itex]
     
  5. Nov 20, 2012 #4

    PeterO

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    Re: HELP!! This is URGENT! How do I solve the nodes and antinodes for this problem??

    That equation gives you the correct answer, but you then interpreted incorrectly.

    The modes of vibration of a string represent STANDING WAVES on the string. The wavelength of a standing wave is 1/2 the wavelength of the travelling wave "causing" the standing wave.

    Your formula gives λ = 6m. That is the travelling wave λ

    So the wavelength of the standing wave is 3m

    The first node is at the fixed end where you start. The next ones are every 3 m from there - until you have reached the other end.

    The anti-nodes are halfway between each of those nodes
     
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