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Gr. 9 Sc. Fair Project: Resonant Frequencies

Dear All:

The following is from an off-line message from Mickey Rowe.  (If you object
Dr. Rowe, you are, of course, free to not post this message.)

> The equations that are explicitly solved to give you the resonant
> frequencies assume that the boundaries of your resonating cavity
> behave as perfect reflectors.  To the extent that that condition is
> violated (e.g. by viscous linings along the walls), the equations
> will give you incorrect answers.  To explicitly solve for the
> resonances given real boundaries is virtually impossible -- most
> people never even see the exact equations unless they take upper
> division (i.e. junior or senior in college) level math, physics or
> engineering courses.  And even there people are taught only how to
> solve the equations under fairly simple conditions.  As you know,
> there are other engineers (my undergraduate degree was
> inbioengineering) on the list, so you *might* get some people to
> help you.

Is there anyone who can help with these equations?  Am I crazy to even think
of trying this with a Gr. 9 math background?  Is there anyone who can
suggest a way to line 3 metres of PVC pipe with a realistic coating?  Would
large diameter rubber hose give a good imitation?

[ I think the bottom line here is whether or not any particular model
  is "close enough".  I recommend that you don't worry too much about
  the "imperfect" walls.  Rather than modify your model, I think you'd
  be better served looking into literature about formants in human
  speech production to see how well people have been able to
  characterize our vocal apparatuses (apparatodes??) using analyses
  similar to what you've already performed for your hadrosaurs.  (I
  should have thought of that yesterday... sorry.)  Unless you're a
  real math prodigy, you're not likely to make much headway trying to
  find exact solutions.  The equations I referred to above are partial
  differential equations.  I really don't think you want to invest too
  much time there because the payoff would probably be pretty small
  relative to your investment.  For others on the list, my version of
  help would have been some quantitation of how much the viscoelastic
  properties of biological tissues and fluids might effect the
  determination of characteristic frequencies of a model hadrosaur
  crest. -- MR ]

Della Drury