Category: Waves

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Solitons

We only address linear media in introductory physics classes, and really only focus on infinite or semi-infinite sine-wave-like disturbances.  In the real world waves have a finite duration; this type of wave is often called a wave packet.  If the wave is large enough, it can be affected by the nonlinear properties of the medium.  The most dramatic example of this is the soliton, a disturbance that propagates with no loss in speed, size or shape over large distances.

Though first observed more than 150 years ago, solitons weren’t understood until the last few decades and are still actively investigated in mathematics, physics and engineering.  This site gives an overview of current research as well as a historical account of the first description of a soliton on a canal in England.

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Tsunamis

A tsunami is an unusually large wave triggered by a major force (usually an earthquake) applied to the ocean.  In the open ocean a tsunami does not have a particularly large amplitude, but its wavelength is enormous.   As it approaches land, the amplitude of a tsunami can increase dramatically, leading to catastrophic flooding.

Several sites, some more media-rich than others, present conclusion about the physics of tsunamis.  The origin of tsunamis is well understood (though, because most are caused by earthquakes, impossible to predict).  Any short, sharp excitation of sufficient size can cause a tsunami; as in many wave-bearing media, the specific details of the excitation are not as important as its total size.

My reconstruction of the major practical difficulties in tsunami warning is

  1. Since the tsunami has a small amplitude in the open ocean, it is difficult to detect before it nears shore, and
  2. Whether a small amplitude open-ocean tsunami turns into a large amplitude wave near shore (called “shoaling”) depends critically on the details of the shoreline and the direction of approach of the wave.  During the time between the triggering of a wave and its arrival on land, there is often not enough information to precisely calculate the threat to populated areas and then to communicate an appropriate warning.  After the fact it is possible to reconstruct the path of the wave, but this is small consolation to the survivors.
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Interactive wave and simple harmonic motion applets

A couple of useful wave simulations, useful if you’re having trouble developing an intuition for the connection between amplitude, wavelength, frequency and speed.

  1. Make your own wave.  Looks like it has some dispersion, so propagating pulses change shape over time.
  2. Several moderately interactive wave simulations.
  3. Reflection as superposition of right- and leftward waves.
  4. Resonance in simple harmonic motion.
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Phononic crystals

Sound waves propagate through air pretty much independently of frequency: if you listen to a sound from a distance, its amplitude is smaller (the sound is softer) but its frequency spectrum is unchanged (the tone is the same).  Everyone who has lived in a dorm knows that certain materials do selectively transmit some frequencies better than others.  That’s why you are woken up by the throbbing bass from your neighbor’s stereo.  This frequency selectivity of normal building materials is pretty crude, however.

Recently, people have built (or actually, discovered) phononic crystals: structures that selectively reflect certain frequencies of sound waves.  Perhaps one day objects will be designed with a particular “acoustic color” as well as particular optical colors.

You can choose a somewhat dry introduction here or a more friendly and colorful summary here; the latter site is labeled ‘vulgarisation’, which I can only guess reveals the author’s ambivalence at making such lofty material accessible to you and me.

If you want to make your own phononic crystal, follow the directions here.

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Galloping Gertie

[youtube]http://www.youtube.com/watch?v=j-zczJXSxnw[/youtube]

This must be the most famous resonance of all time.

If you’ve never seen the 1940 collapse of the Tacoma Narrows suspension bridge, check out one of the many videos of the event, such as this one.

The torsional waves are similar to the  wave demo we have in class, though of course about 100 times larger.

A related phenomenon afflicted the Millenium Bridge in London, though the driving force was footsteps rather than wind and it didn’t lead to catastrophic failure.