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Resonance Speed

  1. Dec 2, 2013 #1
    1. The problem statement, all variables and given/known data

    If a 0.505m long wire is excited into its lowest electrical resonance by a 2.2E7 Hz electrical oscillator, what is the ratio of the speed of the electrical current to that of light? Assume that the wire is like a tube with both ends closed.

    f=2.2E7
    L=0.505
    v=?

    2. Relevant equations

    f=nv/2L
    f=v/λ


    3. The attempt at a solution

    How do I solve this problem if I do not have λ or n? How would the equations work?
     
  2. jcsd
  3. Dec 2, 2013 #2

    CWatters

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    Hint: How would you find λ if this was a problem involving sound waves in an organ pipe? You would do a drawing showing a standing wave with nodes and antinodes then calculate the wavelength.
     
  4. Dec 2, 2013 #3
    How do I know how any nodes and antinodes to draw?
     
  5. Dec 2, 2013 #4

    CWatters

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    The problem states "lowest electrical resonance"
     
  6. Dec 2, 2013 #5
    Does that mean n=1?
     
  7. Dec 2, 2013 #6

    CWatters

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  8. Dec 2, 2013 #7
    It says the fundamental frequency for a closed cylinder is f=v/4L

    Therefore the speed I determine using the formula is...

    v= f*4L = 2.2E7 * 4 *0.505 = 444400000 m/s

    And the ratio of it to the speed of light is:

    444400000 m/s / 3E8 m/s = 0.148

    Does this look correct?
     
  9. Dec 3, 2013 #8

    CWatters

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    I think that's the formulae for a cylinder with one end open and one closed.
     
  10. Dec 3, 2013 #9
    So how do I determine the formula for something closed on both ends?
     
  11. Dec 3, 2013 #10

    CWatters

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    "Closed ends on a tube form a node..."

    Draw it?

    If you looked at the link I gave earlier it shows a drawing for one end open and one end closed. You can see how the formula is derived from that drawing. Do a new drawing with both ends closed and apply same ideas.
     
  12. Dec 3, 2013 #11
    Oh I see, the formula should be f=v/2L
     
  13. Dec 3, 2013 #12
    22220000m/s is the new speed I get?
     
  14. Dec 3, 2013 #13

    CWatters

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    Remember they ask for a ratio.
     
  15. Dec 3, 2013 #14
    Alright makes sense now.
     
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