- #1

- 296

- 0

[tex] D = 17.87 \sqrt[3]{\frac{d}{f^{2}}}[/tex]

Where D is the sphere diameter, d is the diameter of a small circular cavity at the top of the sphere and f is the resonant frequency.

Is it me or is this equation wrong?

The dimensions do not seem to check out. The frequency term introduces a dimension of [itex] T^{2/3} [/itex] to the RHS which is not balanced on the LHS.

I would guess that a term with units of speed squared should be added to the numerator inside the cube-root. That would add dimensions of [itex] L^{2/3} T^{-2/3} [/itex]. I would also suspect that this speed of be the speed of sound in the air (C).

i.e. I think the equation should be:

[tex] D = 17.87 \sqrt[3]{\frac{dC^{2}}{f^{2}}} [/tex]

Can anyone tell me if I'm right?

Thanks