Acoustic resonant frequency of solid 2-sphere?

[Archetype]

I've tried to find the relevant equations on google and wikipedia but have only found the equations for hollow spheres with openings.
Does anybody here know how to calculate it?

[BoilingLeadBath]

Like, inside the hollow of a sphere?

By analogy with a pipe closed at both ends, I'd think that you want a sphere with a diameter equal to ".5*n [n>= 1]" times the wavelength.

Well, maybe. Some of those resonances might not work - just try to imagine a pressure field which supports a 1-wavelength oscillation...
I think this trend continues for all even n.

Note that odd n gives changing-pressure-area in the center of the sphere, whereas even n gives a zero-pressure node in the center. So pumping the even-n resonations, if they can actually exist, might be hard.

[Archetype]

Originally Posted by BoilingLeadBath

Like, inside the hollow of a sphere?

By analogy with a pipe closed at both ends, I'd think that you want a sphere with a diameter equal to ".5*n [n>= 1]" times the wavelength.

Well, maybe. Some of those resonances might not work - just try to imagine a pressure field which supports a 1-wavelength oscillation...
I think this trend continues for all even n.

Note that odd n gives changing-pressure-area in the center of the sphere, whereas even n gives a zero-pressure node in the center. So pumping the even-n resonations, if they can actually exist, might be hard.

Excellent, thanks BoilingLeadBath.

[Zip]

You need more information, the resonant frequency (approximated by natural frequency) requires mass or density and some way to determine stiffness (young's modulus), as well as boundary conditions / dof constraints to avoid rigid body motion.

Considering that a solid sphere is axisymmetric and isotropic, I'm sure you could find an analytical solution with the right equations (the actual acoustic wave equation is a second-order PDE and difficult to solve), but otherwise it's easy enough to do a harmonic response analysis in ANSYS or any other finite element solver to get a very good approximation. With more data as above I can do this for you.

Is this for an engineering application or something else?