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*To*: dinosaur@usc.edu*Subject*: Gr. 9 Sc. Fair Project: Resonant Frequencies*From*: DRURY <drury@agt.net>*Date*: Wed, 15 Jan 1997 17:01:15 -0500 (EST)*Reply-to*: drury@agt.net*Sender*: owner-dinosaur@usc.edu

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 ] Thanks, Della Drury

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