Here we will simulate the dynamics of a torsional wave machine
pictured above. It consists of a set of horizontal rods connected to
one another by a wire. As the rods oscillate in a vertical plane, transverse
waves propagate through the device.
The torsional wave machine illustrates several important physical
concepts.
Forbidden frequency band.
You might expect that waves travel freely from one end of the machine
to the other. It turns out that this expectation works for some
waves but not for others. Waves with low frequencies cannot
travel through it. If you rock one end of the wave machine
periodically and slowly, the other end will remain stationary.
The phenomenon of forbidden frequency bands exist in many other
physical systems. Electromagnetic waves (e.g. visible light)
cannot propagate in metals. The ionosphere reflects back
low-frequency radiowaves. Our wave machine lets you examine how
far a low-frequency wave can propagate into the system before it is
"turned back."
Standing waves. Waves
with sufficiently high frequencies are able propagate through the
machine. In this case we have a further complication: our system
is finite and waves are reflected back at the edges. The
reflections interfere with the original wave and may enhance or
suppress the net amplitude. The highest amplitude is reached when
the original wave and its reflections are matched at their crests and
troughs. In such cases each reflection enhances the net amplitude
of the wave and we find a resonance.
Since it is hard to keep track of multiple reflections, it is more
convenient to think of standing (rather than running) waves. A
resonance corresponds to a standing wave that "fits" in a particular
way between the edges. You can observe resonances visually.
For a more accurate measurement, a second window shows the energy of
the waves as a function of the frequency of the extetrnal force.
For more details about the applet, the physics of the wave machine,
and suggested activities please refer to this
PDF file.
The applet was created with the aid of Easy Java Simulations. Many
thanks to Prof. Francisco Esquembre
for his advice.
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This material is based upon work supported by
the National Science Foundation under Grant No. DMR-0348679.
Any opinions, findings, and conclusions or recommendations expressed
in this material are those of the author and do not necessarily reflect
the views of the National Science Foundation.
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About the author: Oleg
Tchernyshyov is an Assistant Professor in the Department of Physics and
Astronomy at the Johns Hopkins University.