Talk:Wave equation

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Removed

The basic equation is:

v=f\lambda

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.

scalar or vector?

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

Green's function - Lack of proper references.

A new section has been introduced that has some issues regarding relevancy, context (WP:PCR) and lack of references (WP:V) especially regarding claims (WP:NOR) at the beginning of the subsection, e.g.:

[...there are two impulse responses: an acceleration impulse and a velocity impulse. The effect of inflicting an acceleration impulse is to suddenly change the wave velocity $\partial _{t}u$ .]
[For velocity impulse, $s(t,x)=\partial _{t}\delta ^{D+1}(t,x)$ , so if we solve the Green function $G$ , the solution for this case is just $\partial _{t}G$ .]

After addressing the issues with the author directly some improvements have been made regarding adding context to some of the other subsections, but when it comes to providing proper references we unfortunately reached a stalemate. The only reference is a lecture note on the homogeneous wave equation that in no way directly supports the claims regarding the inhomogeneous wave equation.

Given that the author clearly put a lot of effort in writing the subsection, I'd like to ask for opinions of others on this matter. For now I'll just add a {{citation needed}}. Roffaduft (talk) 05:58, 21 August 2024 (UTC)[reply]

Ok, the claims regarding the source terms

s(t,x)=\delta ^{D+1}(t,x)

and

s(t,x)=\partial _{t}\delta ^{D+1}(t,x)

follow by substituting them in the "additional term" given in the "Duhamel's principle" subsection, i.e., they are only part of the solution of the wave equation.

The following statement just introduces a lot of ambiguity IMHO:

Since the wave equation [...] has order 2 in time, there are two impulse responses: an acceleration impulse and a velocity impulse. The effect of inflicting an acceleration impulse is to suddenly change the wave velocity $\partial _{t}u$ . The effect of inflicting a velocity impulse is to suddenly change the wave displacement $u$ .

First, because it fully ignores the initial conditions of

u

and

\partial _{t}u

and, second, because either choice of source term

s(x,t)

can (indirectly) affect both the displacement and velocity of the wave. Roffaduft (talk) 08:55, 22 August 2024 (UTC)[reply]

Explanation of wave equation is not right

Some of the explanation of the wave equation is not correct, or at least is written from a much more casual tone than the rest of the article. For example it actually uses the word “pointy” in reference to potentials u with very high second derivatives. Unless anyone objects, I’ll clean this up in a second, and I would appreciate it if someone could review what I replace the current explanation with. OverzealousAutocorrect (talk) 02:58, 26 August 2024 (UTC)[reply]

WP:BOLD, just assume you did a good job when nobody responds to your edits.

I think the whole article could use a good cleanup/restructuring. For example:

There is an "introduction" subsection after the introduction
The article goes from 1D to 3D to 2D to multi-D
Too much emphasis on scalar/vector in the subsection titles IMHO
The sections on the inhomogeneous wave equation are a bit blehh.
The referencing is pretty horrible throughout the article.

If you're willing to work on the "introduction" subsection, I'd love to help out. Maybe we can move some of the general introductions to the actual intro of the article, e.g, introduce the distinction between vector and scalar over there to allow reorganising the rest of the article and changing some of the subsection titles. Roffaduft (talk) 07:35, 26 August 2024 (UTC)[reply]

Vote to remove "Investigation by numerical methods" subsection

I'd like to remove the subsection Investigation by numerical methods from the article. It's just a crude example of a numerical method applied to the wave equation. It does not provide insight or unique information regarding the wave equation nor does the wave equation leads to some unique application of a numerical method.

If there are no objections, I'll remove the subsection in due time. Roffaduft (talk) 10:27, 26 August 2024 (UTC)[reply]