Talk:Wave equation

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Removed:

The basic equation is:

v = fλ
I'm not sure it should be removed. Although "perfectly correct", it's the same as listing the differential-only forms of Newtonian mechanics -- correct, but not useful.
Perhaps you (or I) should add it back in a section describing specific solutions, such a standing wave patters, or in this case, singletons.

Fair enough. as it stood it was confusing and seemed unrealed to the differential equation this article is about -- Tarquin 13:11 Jan 6, 2003 (UTC)

Not sure if this is the right way to suggest this,(bit of a beginner with wikipedia) -- surly the above formula should be in the article as it's the basic formula and very widely used, i was looking for it when i searched "wave equation". Sorry again if this is the wrong way of suggesting.

Contents

[edit] Elastic eqn

I added the elastic eqn, but network difficulties meant I wasn't logged in.Gwimpey 05:26, Mar 5, 2005 (UTC)

[edit] scalar or vector?

the function in search, u, is scalar or vector-valued? i.e. when is it what?

[edit] Culture

I've heard that Laplace was riding his horse next to a river when something big fell in the water. The waves propagated to the riverbanks and down the river. Laplace noticed that there was a wave that persisted, never dying out as long as he followed it. It is said that this inspired him to study waves mathematically. Does anyone else know about this? --Orthografer 16:30, 15 December 2005 (UTC)

What he saw is I think a soliton. I heard something similar a while ago. I guess it belongs to the same category of stories as Newton's apple. Might be true. Oleg Alexandrov (talk) 19:52, 15 December 2005 (UTC)
It wasn't Laplace, it was a fellow called Russell; it wasn't an object, it was a barge being towed by mules which suddenly stopped. He saw the water gather up at the prow of the boat, and detach itself into a single solitary wave, which then proceeded quite repidly down the canal. He chased the soliton on horseback for 17 2 miles (!). Its all written up in an account, presented to some or another scientific society; its mentioned in many books. The math is given by the KdV equation. linas 18:58, 1 June 2006 (UTC)
Why, WP has an article on it: John Scott Russell; see also the external link therein. linas 19:00, 1 June 2006 (UTC)
Thank you! Orthografer 20:38, 2 June 2006 (UTC)

I intend to add material on the 3-D case, with emphasis on domain of dependence, Huygens' principle, etc. The 2-D case can then be teated by method of descent. Donludwig 18:03, 31 March 2006 (UTC)

[edit] Delta, Nabla and Notation

Can someone modify this article to explain what the heck Δ stands for, in that first equation? linas 18:58, 1 June 2006 (UTC)

Added identification of Δ in the equation, along with the alternative \nabla^2 form, as the Laplacian and an added appropriate link. --Nkrupans 16:10, 7 June 2006 (UTC)

A broader question of notation, does anyone else find the \nabla^2 more used/familiar than the Δ for the Laplacian operator? Looking through the physics articles on Wikipedia, the \nabla^2 seems dominant. I mention this in the discussion page for the Laplacian and may open up a new topic there about the notation. Let me know what you think. --Nkrupans 16:41, 7 June 2006 (UTC)

My two cents: my personal preference is the \nabla^2 form, though I speak only for myself. For me, it's simply easier to remember exactly what it is that way ( that is \nabla^2 suggests to some extent \vec \nabla \cdot \vec \nabla ). Anyway, that's my opinion. DAG 08:31, 17 June 2006 (UTC)

[edit] Added Section on In-homogenous W.E. in 1D

I added a section on how to get a solution to an in-homogenous wave equation initial value problem. In one dimension. It's better than none I suppose...  :) DAG 10:30, 17 June 2006 (UTC)

I did a small copyedit and noticed you called the initial condition f the source function. I believe the correct interpretation is that the inhomogeneous term s is the source function. Someone should correct me if I'm wrong and list a source within this section, perhaps Boyce and DiPrima's book if it has the relevant material. Orthografer 20:22, 17 June 2006 (UTC)
No, no, you're completely right, that was my mistake. I initially started by using f as the source function, but to remain consistent with the rest of the article, I wanted to use the same symbols for the initial conditions, so then I had to change f. Apparently I wasn't completely thorough...  :/ Oops. DAG 21:26, 17 June 2006 (UTC)
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