Spheres octaves and pitch

  1. Feb 10, 2008 #1
    Dose anyone know the relationship of cube root numbers and the fraction of 1/8

    "Assuming a body of a size represented by X has a pitch of 1024 per second, then a pitch of 2048 (double 1024) per second will be produced by a body having a volume of some mean between 1/8 of X and the cube root of X"

    I understand why a pitch double the original will be produced by a sphere 1/8 the volume because if you double the diameter of a sphere you increase its volume by eightfold.

    I don't however understand the relationship between 1/8 and cube root numbers, any ideas?
     
    Last edited: Feb 10, 2008
  2. jcsd
  3. Feb 10, 2008 #2

    pam

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    The pitch depends on the radius of the sphere. Doubling the radius multiplies the volume by
    2^3=8.
     
  4. Feb 11, 2008 #3
    Is it as simple as that...haha lol, I knew 2^3 was 8 but I had assumed I was looking for something more complex, funny when you look for the complex you miss the simple.

    Would this only work for spheres then?
     
  5. Feb 11, 2008 #4

    clem

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    Science Advisor

    It would also work for the frequencies of a 3D object. For a drumhead, the pitch would go like 2^2.
     
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