While we're on the topic of cylinder wall resonance I thought I should
mention a simple demonstration a colleague at Oxford, a chemist, showed
me. Place an empty cylindrical coffee mug on a tabletop with its handle
pointing north. Using a spoon handle or other hard metal object tap the
south edge of the lip of the cup sideways and listen to the note
produced. Now try tapping at different azimuths, notably the cardinal
points and the points midway between them (e.g. SW, NE, etc.). If you
find a good mug you will hear a difference between the cardinal points
and the midway points of as much as a semitone, a frequency difference
of more than five percent.
The explanation of this phenomenon is easy and elegant. I won't spoil
the discussion by giving it here; I want you to do the experiment! As
Ron will point out, this is an example of what is called "symmetry
breaking" elsewhere. I bring it up here because the oscillatory modes
of a beaker are the same, and they exhibit the same symmetry breaking
phenomenon (to a lesser extent) as the coffee mug. Incidentally, we
too break both beakers and wine glasses here at Simon Fraser. Sometimes
we use sound.
Leigh
(The Oxford chemist is Peter Hore. His wife, Julia Yeomans, an Oxford
theoretical physicist, may have helped him a bit; I don't know.)