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I Meaning of the word "Harmonic" in different contexts

  1. Aug 24, 2017 #1


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    A harmonic function is one that satisfies Laplace's equation -- a definition cannot be more precise than that.

    However, in the study of vibrations, sine and cosine are considered harmonic functions; but they don't solve Laplace's equation.

    And then there are words like: harmonics (for higher frequencies) or "harmonic oscillators" that repeat their motion.

    Could someone provide a suite of definitions of the word harmonic?

    At the moment, I am confused and thinking that the functions that solve Laplace are related to harmonic oscillators. Am I dealing with multiple definitions?
  2. jcsd
  3. Aug 24, 2017 #2


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    Staff: Mentor

    Probably. It's an unfortunate and confusing fact of life that many words have different meanings or definitions in different contexts.
  4. Sep 27, 2017 #3
    I'd guess that harmonic in each case may have a common etymology from stringed instruments.

    The wikipedia article here makes the connection between the harmonic series in music, harmonic mean, harmonic oscillators, etc. I don't know about the Laplace's equation piece of it though.
  5. Sep 27, 2017 #4


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    Science Advisor
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    Talk aboutthe use of the term " Normal" in Mathematics: https://en.wikipedia.org/wiki/Normal#Mathematics

    Talk about overloading notation.
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