In Module C we reviewed wave behavior and saw that the defining property of a wave is the property of interference. A natural outcome of this interference property is a standing wave. Standing waves are formed when a traveling wave interferes with it own reflection. At certain frequencies (dependent on the physical parameters of the situation) the interfering waves set up a series of nodes and antinodes.
Let us have a look at some standing waves more closely. In the following video clips a light string is attached to a modified audio speaker. A signal generator causes the speaker to vibrate at a known frequency that in turn vibrates the string.
Move the mouse cursor left to right in the video window to play the video.
Fundamental
1st Harmonic
2nd Harmonic
3rd Harmonic
After studying the videos please answer the following questions:
How is frequency related to the length of the wave (approximately)?
How is the wavelength related to the length of the string?
The following web page has some standing wave simulations, just ignore the complex mathematics and look at the animations.
http://physics.usask.ca/~hirose/ep225/animation/standing1/anim-stwave1.htm
The most famous standing wave in history would have to be the Tacoma Narrows Bridge. This suspension bridge was affected by wind, which at certain speeds set up standing waves along the bridge's structure. To learn more about the Tacoma Narrows have a look at the web pages below. You can down load a mpeg video file of the bridge collapse from these site.
http://www.enm.bris.ac.uk/research/nonlinear/tacoma/tacoma.html http://www.firebirdz.net/tnb/
Standing waves, or waves fitting into a region where it is trapped, applies to all waves including matter waves.