The common mathematical derivation predicts frequencies needed for standing
waves on a string (this week lab using Pasco's oscillator). But it tells me
nothing about amplitudes (which are larger than the amplitudes of the
vibrating rod).
To demonstrate resonances at predicted frequencies students must be lucky
to choose strings of correct linear density and right tension forces. For
too large f, amplitudes are so small that loops are practically invisible.
To avoid frustration I tell them exactly what to do and experiments are
succesful.
But for my own satisfaction I would like to know how to choose the right
tension force, the right string and the right frequancy to have the largest
possible amplitudes. This would eliminate the "trial and error"approach which
is not as glamoures as a numerical prediction based on reasoning. And I would
also like to know, before the experiment, how large amplitudes are expected
at each resonance.
I know the terms "Q value" and "impedence matching" but I not enough to
make numerical predictions in my situation. Any help?
Ludwik Kowalski