Derivation of Equations of Resonance

[roldy]

For a vibrations lab experiment, our group decided to determine the resonance of 3 wines glasses, conical, cylindrical, spherical. I know that on Wikipedia they have these equations. What they don't have is how they derived them. I would like to know the math behind these. I've tried searching on the web but to no luck. Is there any place I could find out more or does anyone here know anything about them? Thanks for any help

 

[FredGarvin]

You need to look at the 1D or 2D wave equation and solve that using the particular boundary conditions. It would be a big help if you knew separation of variables method for solving PDEs

http://en.wikipedia.org/wiki/Acoustic_wave_equation