Timeline for Wave equations & propagation theories
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Jun 11, 2013 at 9:46 | vote | accept | Raven | ||
| Jul 2, 2011 at 15:25 | history | tweeted | twitter.com/#!/StackPhysics/status/87180175309160449 | ||
| Jun 28, 2011 at 23:39 | comment | added | Willie Wong | If you actually solve the wave equation in 2D ($\partial_t^2 u = c(\partial_x^2 u + \partial_y^2 u)$) numerically, you will be able to incorporate diffraction automatically. Refraction can be handled by changing the wave-speed $c$ between different media (but you need to implement boundary matching rules to properly capture the effect of the wave being partially transmitted and partially reflected). | |
| Jun 28, 2011 at 23:36 | comment | added | Willie Wong | If you just want to exhibit wave phenomenon, you can do worse than just solving the linear wave equation numerically. You can try to do some sort of ray tracing via Huygen's principle, but in two dimensions it won't properly demonstrate the interior tail effect of the waves. Furthermore, while ray tracing can give you normal propagation and reflections, and it can to some extent (using Snell's law) deal with refractions, it cannot deal well with diffractions. | |
| Jun 28, 2011 at 21:26 | comment | added | Raven | Well I can show you: youtube.com/watch?v=5Xf-Xt_L2GQ&feature=channel_video_title . This is my first simulation, where I used just that linear equation I mentioned above and it works really fine - until you need to reflect, make shadow, difract or refract.. Actually I was able to create model using same technique working for the first 3 phenomenons, but I couldn't use it for refraction and it was quite complicated so I started from scratch - now searching for basic equations and building new model on top of those. | |
| Jun 28, 2011 at 19:52 | answer | added | BebopButUnsteady | timeline score: 1 | |
| Jun 28, 2011 at 19:49 | answer | added | Vintage | timeline score: 1 | |
| Jun 28, 2011 at 19:49 | comment | added | Willie Wong | Also: If you say more about what you are trying to simulate, maybe it would be easier (for readers) to suggest an appropriate model? | |
| Jun 28, 2011 at 19:47 | comment | added | Willie Wong | If you want something appoximated by the linear wave equation, what you are looking for is the "fundamental solution" of the wave equation. If you google that you'll find lots of information. In the case of 3 (and other odd numbers) of spatial dimensions, for solution of the wave equation Huygen's principle is strong, in the sense that if you give a point perturbation there should in fact be nothing inside the envelope: the wave only lives on the wavefront. Compared against physical waves, this may suggest that the linear approximation is not the right one. | |
| Jun 28, 2011 at 19:43 | comment | added | Vintage | @dmckee: Thank you so much for that explanation. I had tried to make Mathjax work, to no avail. I will try again, while also attempting to answer Raven's question. | |
| S Jun 28, 2011 at 18:05 | history | suggested | lurscher | CC BY-SA 3.0 |
refactored formula as MathJax
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| Jun 28, 2011 at 17:55 | review | Suggested edits | |||
| S Jun 28, 2011 at 18:05 | |||||
| Jun 28, 2011 at 17:41 | comment | added | dmckee --- ex-moderator kitten |
BTW: This site uses MathJax (a LaTeX alike math rendering egine) so you can write $A \sin(kx - \omega t + \phi)$ and similar expressions (that is A \sin(kx - \omega t + \phi) enclosed in dollar signs). You find a bare minimum of help in the FAQ.
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| Jun 28, 2011 at 17:13 | history | asked | Raven | CC BY-SA 3.0 |