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Calculating number of harmonics problem

  1. Nov 6, 2012 #1
    The frequency of the highest note on the saxophone is 1,568 Hz.
    1.How many harmonics of that note can we hear?
    2.How many harmonics of the note one octave below it can we hear?

    I didn't put the title in correctly on my first thread, so calm down everyone. But my book aint helping me much on this problem, so some help would be great
     
  2. jcsd
  3. Nov 7, 2012 #2
  4. Nov 7, 2012 #3

    PeterO

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    You also need to know whether a Saxophone acts as an open or stopped pipe, because if it acts as a stopped pipe then only the odd harmonics will be sounded.

    A clarinet for example behaves as a stopped pipe in its lower register and an open pipe in its upper register. I am not familiar with the characteristics of a saxophone.

    The harmonics of the sax will also be influenced by the end correction of the instrument too.

    Then again, perhaps the question is just asking about harmonics of the fundamental frequency of the Sax - independent of the actual instument. Harmonics are, after all, just arithemtic. (As distinct from over-tones)
     
  5. Nov 8, 2012 #4
    As a first approximation the 1568Hz sound pressure wave of the saxophone can be approximated by a single pure sine wave of frequency 1568Hz. As the wave is not a pure sine wave but slightly distorted sine wave we must add higher harmonics to better approximate the sound pressure wave.

    Sound pressure = a1*sin(f) + a2*sin(2f) + a3*sin(3f) + a4*sin(4f) + ...

    Where f = 1568Hz

    Aren't these the harmonics the question asks about?
     
  6. Nov 8, 2012 #5

    PeterO

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    Certainly they represent the set of harmonics of 1568 Hz

    The question states: 1.How many harmonics of that note can we hear?

    The range of human hearing will determine the highest one we could possibly hear - one of the harmonics is 15680 Hz, another is 156800 Hz, yet another 1568000 Hz. Can the human hear those very high frequencies?

    Secondly, are we being asked "How many harmonics of that note can we hear?" produced by the saxophone playing its highest note. That is where we need to know whether it is behaving like a stopped pipe or an open pipe, and what effect end correction will have (if any).
     
  7. Nov 8, 2012 #6
    Hey, thanks for the replys I ended up figuring it out. 20000Hz/1568Hz and it gave me the right answer of 12 harmonics.
     
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