Wave Envelope: Difference between revisions
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(Created page with " thumb|left A simple demonstration of the distinction between a wave envelope and individual wave crests. The red curves depict the wave envelope...") |
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=== Derivation with KdV === | |||
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== More Examples == | == More Examples == | ||
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|+Various Demonstrations of Wave Envelope vs. Wave Crest Propagation | |+Various Demonstrations of Wave Envelope vs. Wave Crest Propagation | ||
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| Case | ! scope="col" width="75px" | Case | ||
| Continuous Wave Train | ! scope="col" width="200px" | Continuous Wave Train | ||
| Solitary Wave | ! scope="col" width="200px" | Solitary Wave | ||
|- | |- | ||
|<math>c_g>c_p</math> | |<math>c_g>c_p</math>: Envelope propagation faster than crest propagation. | ||
| [[File:wave_envelope_s1.gif|thumb|]] | | [[File:wave_envelope_s1.gif|thumb|center|]] | ||
| [[File:wave_envelope_g1.gif|thumb|]] | | [[File:wave_envelope_g1.gif|thumb|center|]] | ||
|- | |- | ||
|<math>c_g=c_p</math> | |<math>c_g=c_p</math>: Envelope propagation equal to crest propagation. | ||
| [[File:wave_envelope_s2.gif|thumb|]] | | [[File:wave_envelope_s2.gif|thumb|center|]] | ||
| [[File:wave_envelope_g2.gif|thumb|]] | | [[File:wave_envelope_g2.gif|thumb|center|]] | ||
|- | |- | ||
|<math>c_g<c_p</math> | |<math>c_g<c_p</math>: Envelope propagation slower than crest propagation. | ||
| [[File:wave_envelope_s3.gif|thumb|]] | | [[File:wave_envelope_s3.gif|thumb|center|]] | ||
| [[File:wave_envelope_g3.gif|thumb|]] | | [[File:wave_envelope_g3.gif|thumb|center|]] | ||
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Revision as of 11:28, 2 June 2015
A simple demonstration of the distinction between a wave envelope and individual wave crests. The red curves depict the wave envelope, while the blue curve indicates the individual wave crests (in the context of a surface wave, the blue curve can be viewed as the water surface).
The blue curve is not propagating while the red curve is steadily propagating to the right, highlighting the distinction between the propagation of an individual wave crest.
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Derivation with KdV
To be included...
More Examples
| Case | Continuous Wave Train | Solitary Wave |
|---|---|---|
| : Envelope propagation faster than crest propagation. |  |
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| : Envelope propagation equal to crest propagation. |  |
 |
| : Envelope propagation slower than crest propagation. |  |
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