| MadSci Network: Physics |
Meagan, I think this is a quite interesting topic that you are investigating. I remember the wine glass and other related demonstrations particularly from my physics classes. From my perspective there are two general means of calculating an object’s resonant frequency. For a fairly simple object it is possible to derive equations that describe the frequency of resonance and also the way the object vibrates. In the physics biz we call the resonant frequency an eignevalue, and the way the object vibrates an eigenmode. The word “eigen” is a German word which you can look up! :-) Note that even a simple object can have more than one resonant frequency. When I say simple, I mean like a pendulum swinging in a small arc, or a weight hanging from a spring, or an aluminum rod, or a round metal plate. The math you typically get as a senior in school should be able to handle the first two cases. The last two cases require math seen after a year or three of college. Things you might look up include vibrational modes, Bessel functions, and Chladni plates. For most objects in the real world we have to use a computer simulation to find the resonant frequencies. You would build up a model of the object that you are interested in on the computer. One way to do this is with something called finite element analysis, where you make a model where your object is made up of a large number of simple shapes connected together that can move slightly relative to each other. Then you apply equations of motion to the model and try to identify resonant modes. This sort of analysis can take alot of computer power. In the MadSci answer that I reference below , there is a link to finding the resonant modes of the hood of a Mazda 323. For your second question the answer is yes, other types of glass will work. About 200 years ago when the instrument know as the glass harmonica was first developed, many different types of glasses were used for the cups of the instrument. At present, the preferred material is pure quartz (SiO2). A really good demonstration that uses metal involves a smooth metal rod made from aluminum. If the rod is clean and smooth, and you rosin your fingers, you can make the rod “sing” by smoothly dragging your fingers over the rodl See this MadSci question: 889395376.Ot See these links http://whiplash.stanford.edu/MIT/html/wineglass-resonance.html www.finkenbeiner.com/harmonica.html www.finkenbeiner.com/article1.html www.geocities.com/Vienna/7597/ www.mip.berkeley.edu/physics/B+55+10.html Regards, Everett
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