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accoustical factorization?

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  • Johannes Z.
    I´d like to share a little concept for ACCOUSTICAL FACTORIZATION by using the relation between tones and overtones on strings, many guitarplayers might be
    Message 1 of 3 , Jul 11, 2007
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      I´d like to share a little concept for ACCOUSTICAL FACTORIZATION by
      using the relation between tones and overtones on strings, many
      guitarplayers might be familiar with: Maybe its useful for someone of you?

      Imagine a string swinging in the fundamental frequency. You can
      theoretically create additional overtones for example on a guitar by
      touching the string slightly at any point you wish.(Practicaly only
      overtones with high amplitudes might be hearable by ear, so the number
      of playable Overtones is limited; see also
      http://en.wikipedia.org/wiki/Overtone )

      An Overtone is created by dividing the fundamental Oscillation of the
      string in a bunch of standing waves with the same wavelenght each.

      What does it have to do with Factorization?

      Explanation by example:

      1. Add to the fundamental oscillation of a string an oscillation of
      187 standing waves by creating an Overtone with wavelenght of 1/187
      stringlenght.

      2. Try to create as much additional overtones you can with the
      IMPORTANT PREMISE, that you search these Overtones only by touching
      the allready existing wavenodes. (So touch the string at 1/187, 2/187,
      3/187, but NOT for example at 2,5/187)

      3. You will find out that under these circumstances the string allows
      only the following three Overtones:

      Overtone with wavelenght 1/187 (187 standing waves)
      Overtone with wavelenght 11/187 (17 standing waves)
      Overtone with wavelenght 17/187 (11 standing waves)

      4. Interpreting this result in mathematical terms will wake you up,
      right?: 187=11*17
      Surely it works in theory with any possible "Overtone-Composite", as
      long as the Premise mentioned above is taken into account.
      Anyway, the search for overtones in that way still works like trying
      out every divisor of 187, so it doesnt seem to be spectacular and is a
      slow way of factorization.

      5. More intersting might be the following way:
      -Create the Overtone 1/187 first by external stimulation, DONT start
      with the fundamental resonance.
      -Now "shake" the whole string and add in that way so much energy, that
      at some point the absorption of energy within the amplitude of the
      allready existing standing wave comes to its limits
      -Now the string will try to "swing" in all other possible frequencys,
      while the allready existing wavenodes are the most stable and the
      wavemaxima are the most vulnerable parts of the string regarding
      additional "swingmodes".
      -Guess what additional Overtones will arise first...

      =P

      Sorry to bother you with so much text, I hope I get some replys
      nonetheless. Is it intersting? Does it fit in any formula? Do you have
      hints for me where to read further or something like that?

      Cheers

      Johannes

      In case have an additional look at
      http://en.wikipedia.org/wiki/Standing_wave
      and
      http://en.wikipedia.org/wiki/Overtone
      and
      http://en.wikipedia.org/wiki/Oscillation
    • scolnik
      PHYSICS: Factoring Numbers with Waves Zubairy Science 27 April 2007: 554-555 DOI: 10.1126/science.1140915 Hugo Scolnik A wise man hears one word and
      Message 2 of 3 , Jul 12, 2007
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        PHYSICS: Factoring Numbers with Waves
        Zubairy
        Science 27 April 2007: 554-555
        DOI: 10.1126/science.1140915

        Hugo Scolnik

        A wise man hears one word and understands two.



        [Non-text portions of this message have been removed]
      • Johannes Z.
        Hugo Thank You for the hint, I´ll have a look at it soon as I get free access somewhere...
        Message 3 of 3 , Jul 12, 2007
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          Hugo

          Thank You for the hint, I´ll have a look at it soon as I get free
          access somewhere...

          --- In primenumbers@yahoogroups.com, "scolnik" <scolnik@...> wrote:
          >
          > PHYSICS: Factoring Numbers with Waves
          > Zubairy
          > Science 27 April 2007: 554-555
          > DOI: 10.1126/science.1140915
          >
          > Hugo Scolnik
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