How Do Cube Root Numbers Relate to the Fraction 1/8 in Determining Pitch?

[PH7SICS]

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?

 

[pam]

The pitch depends on the radius of the sphere. Doubling the radius multiplies the volume by
2^3=8.

 

[PH7SICS]

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?

 

[Meir Achuz]

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