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Standing Waves

  1. Feb 7, 2009 #1
    1. The problem statement, all variables and given/known data
    Given the first harmonic, with length L, of a certain standing wave, what is the process for coming up with the next 3 harmonics for it?


    2. Relevant equations
    velocity = wavelength * frequency


    3. The attempt at a solution
    I don't understand how to draw the "next harmonic". I've come up with a formula for wavlenth of the first harmonic:
    = (4/3)L
    and with that, frequency
    = (3v)/(4L)
     
    Last edited: Feb 7, 2009
  2. jcsd
  3. Feb 7, 2009 #2
    Take a butchers at this...

    http://id.mind.net/~zona/mstm/physics/waves/standingWaves/standingWaves1/StandingWaves1.html" [Broken]
     
    Last edited by a moderator: May 4, 2017
  4. Feb 7, 2009 #3

    AEM

    User Avatar

    Well, for a standing wave the ends are fixed and therefore are nodes. In a sinusoidal wave the nodes are half a wavelength apart. In a string of length L, standing vibrations may be set up by different frequencies that give rise to waves that will have nodes at the endpoints. These wave will have wavelengths,

    [tex] \lambda = 2L, \frac{2L}{2}, \frac{2L}{3},..., \frac{2l}{n} [/tex]

    The wave speed c is the same for all frequencies, and as you say, [tex] c = f \lambda [/tex]

    This should be enough for you to deduce the frequencies and the wavelengths of the harmonics (or overtones as they are sometimes called).
     
  5. Feb 7, 2009 #4
    So as I've said that the wavelength of the first harmonic =(4/3)L, that means the wavelength of the second harmonic
    = (4/3)L / n = (4/3)L / 2 = (2/3) L

    Is this right?

    By the way, the wave has a node at one end and is open at the other. In class we learned that standing waves with one open/one fixed end have only odd numbered harmonics. Why is this?
     
    Last edited: Feb 7, 2009
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