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Spheres octaves and pitch

by PH7SICS
Tags: octaves, pitch, spheres
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PH7SICS
#1
Feb10-08, 11:15 AM
P: 23
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?
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pam
#2
Feb10-08, 05:19 PM
P: 455
The pitch depends on the radius of the sphere. Doubling the radius multiplies the volume by
2^3=8.
PH7SICS
#3
Feb11-08, 05:58 AM
P: 23
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?

clem
#4
Feb11-08, 12:49 PM
Sci Advisor
P: 1,269
Spheres octaves and pitch

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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