How to Catch a Standing Wave
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This Demonstration illustrates a concept from classical physics that also applies in quantum mechanics: quantization. This phenomenon takes place when waves on a string with fixed points resonate and, in order to prevent destructive interference, a specific geometrical requirement needs to be met. In this case, an integer multiple of half-wavelength needs to be contained between the fixed ends. Similar principles apply to many musical instruments, for example, guitar strings [1].
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Contributed by: D. Meliga, S. Z. Lavagnino and A. Ratti (September 2017)
Open content licensed under CC BY-NC-SA
Snapshots
Details
Snapshot 1: forbidden standing wave; in order for it to be allowed, it is necessary to change the frequency or the string length (dragging the locator or by means of the "first harmonic" control)
Snapshot 2: the third harmonic is displayed
Snapshot 3: in this case, the number of nodes is too high to show the fundamental frequency; however, this shows a generic resonant condition
References
[1] G. C. Pimentel and R. D. Spratley, Understanding Chemistry, San Francisco: Holden-Day, 1971.
[2] The Physics Classroom. "Formation of Standing Waves." (Sep 13, 2017) www.physicsclassroom.com/class/waves/Lesson-4/Formation-of-Standing-Waves.
Permanent Citation
"How to Catch a Standing Wave"
http://demonstrations.wolfram.com/HowToCatchAStandingWave/
Wolfram Demonstrations Project
Published: September 20 2017