Bill Beaty's note may have led some to believe that standing waves are
not important in the understanding of the motion of a plucked string
which is stopped at both ends. Nothing could be further from the
truth. The motion of such a string in the ideal case can be decomposed
entirely into harmonic standing waves with nodes at the ends of the
string. The travelling pulses described by Bill and Mark can be
reproduced by the superposition of many such standing waves. If you
wish to do so you may choose to treat these standing waves as a mere
mathematical fiction, but the basilar membrane in your cochlea will
readily decompose the auditory results and produce their fourier
decomposition on your auditory cortex. That is real enough for me!
Mark, the cable you played with is not an ideal taut string for a
couple of reasons. An ideal taut string is perfectly limp; it does not
provide a restorative stiffness when it is bent, as wire rope does.
The ideal taut string moves under the influence of restorative forces
due to a hypothetically constant tension in the string. Your wire rope
had a tension which varied due to gravity, the tension being much
higher at the upper end than at the lower. The high pitched precursor
to the main pulse is likely due to the transmission of longitudinal
modes in the cable at speeds higher than those of the transverse mode.
Your action in whacking the cable with a piece of firewood is entirely
understandable and appropriate; I would have done the same thing, and
I encourage my students to seek out acoustic phanomena everywhere in
just that manner. I once almost got into trouble doing this in the
Statue of Liberty while standing in line. Did you know that the Statue
is a fairly high-Q structure? It hangs by some highly elastic cables
from a base structure, and it can be set into vertical oscillation by
periodically pushing sideways on any one of them with the proper
frequency and phase. It was very easy to get an amplitude of a couple
of millimeters, but my wife made me stop when other people on the
stairs began to notice the motion. Another of my favorite resonance
demos involves tall light standards or tall, thin, straight dead or
defoliated trees.