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Constituent traveling waves and strings and vibrations

  1. Dec 29, 2008 #1
    1. The problem statement, all variables and given/known data

    A 30-cm long string, with one end clamped and the other free to move transversely, is vibrating in its second harmonic. The wavelength of the constituent traveling waves is:
    A) 10 cm
    B) 30 cm
    C) 40 cm
    D) 60 cm
    E) 120 cm

    2. Relevant equations

    [tex]L = n(\frac{1}{4}\lambda)[/tex]

    3. The attempt at a solution

    First, what I tried was this:
    [tex].30 = 2(\frac{1}{4}\lambda)[/tex]
    [tex]\lambda = .60[/tex]

    The answer, however, was C) 40 cm.

    So, when I changed 2 to 3, like this:

    [tex].30 = 3(\frac{1}{4}\lambda)[/tex]
    [tex]\lambda = .40[/tex]

    I got the correct answer.

    So, does the constituent traveling wave mean the wave with the next harmonic number? Somehow, I don't think that is correct. Constituent means 'component' and such.

    I don't understand the concept behind this, why do you use the harmonic number of 3?
     
  2. jcsd
  3. Dec 30, 2008 #2

    Redbelly98

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    Science Advisor
    Homework Helper

    It looks like by "harmonics", they mean only the allowed vibration modes and not simply multiples of the lowest-frequency mode.

    You might try drawing a sketch of the "modes" or shapes of the string for n=1, 2, and 3. See if it makes sense that the n=2 case is not valid, given the condition of 1 fixed + 1 free end.
     
  4. Dec 30, 2008 #3
    Ah I see, since it's clamped at one end it can only have odd number harmonics correct? So the second harmonic they would mean n=3.
     
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