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Standing Waves and Harmonics

  1. Sep 24, 2004 #1

    We just did a lab on waves and one in particular I'm unsure about.

    We set up standing waves on a spring and observed the period of each successive harmonic.

    It was found that the period was cut in half with each harmonic. Or the frequency was doubled. ie. harmonic 1 produced one standing wave with a frequency of f, harmonic 2 produced two standing waves each having a frequency of 2f, harmonic 3 produced three standing waves each having a frequency of 3f, etc.

    It was also found that the wave speed of each wave was (wave length / period) about the same in each case. The spring was 4 m, the first harmonic produced a wave length of 8 m, the second of 4 m, the third of 2.67 m, and the fourth of 2 m.

    I am expected to discuss what I have shown by doing this.

    Here is what I am thinking, but I am unsure as to whether or not I'm correct:

    In each harmonic, the same energy is distributed in the spring and so in each standing wave. Since the same energy is in each standing wave, the frequency of the first harmonic is f having a speed of v. In the second harmonic, there are two standing waves and so the energy is distributed equally, so the frequency of each wave will be twice as much; in other words, the period T will be half as much in each standing wave to make an overall value of T, or 1/f. The wave speed remains the same in each case because each wave is moving with the same speed, because the spring as a whole is moving with the same speed.


    Another thing, we had to measure the speed of a pulse which we sent down the spring, let's say it was x. How does x apply to what's been performed?

    x ~ 5 m/s (4 m, 0.85 s for pulse)
    v ~ 8 m/s (wave speed, about the same for each +/- 1 m/s)

    T1 ~ 1.2 s (period of first harmonic)
    T2 ~ 0.6 s
    T3 ~ 0.3 s
    T4 ~ 0.15 s

    Thank you very much!
    Last edited: Sep 24, 2004
  2. jcsd
  3. Sep 24, 2004 #2


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    Are these transverse waves or longitudinal waves? (Just curious!)

    Also, you aren't dealing with multiple "standing waves" in any of those cases. You are dealing with a single standing wave with multiple nodes!

    Try thinking of each standing wave as being composed of two travelling waves moving in opposite directions.
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