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.

torsional wave machine

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.


Ejs
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. 

About the author: Oleg Tchernyshyov is an Assistant Professor in the Department of Physics and Astronomy at the Johns Hopkins University.