Talk:Wavelength/Archive 2

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Work needed to treat more general waveforms

A beginning on this topic has been made, but more is needed. Brews ohare (talk) 00:43, 11 June 2009 (UTC)

The concept of wavelength is most often applied to sinusoids. More is only needed if we have good sources that make the more general case seem important. Dicklyon (talk) 00:47, 11 June 2009 (UTC)

I did some looking, and found that that concept is used in ocean engineering and such; it doesn't work in linear dispersive media, but does for water surface waves. So I made a section an added a ref. Dicklyon (talk) 01:24, 11 June 2009 (UTC)

A general waveform can be found almost anywhere, especially if you are looking at spatial variation. IMO it is nutso to present results for a specialized case when they are very simply derived for a general case that actually makes the concepts clearer and promotes some imagination about their usefulness. Brews ohare (talk) 03:31, 11 June 2009 (UTC)

In physics, the more usual view is that a general waveform is composed of a sum of sinusoidal waves. The wavelengths of a general waveform are the wavelengths of its component sinusoids, which are given by Fourier analysis. One can only meaningfully talk about the wavelength of a general waveform if the medium in which it propagates is non-dispersive, since in a dispersive medium a non-sinusoidal waveform changes shape as it propagates.--Srleffler (talk) 04:16, 11 June 2009 (UTC)

These points are raised in the article already. Brews ohare (talk) 14:40, 11 June 2009 (UTC)

Brews, your re-write of the "general waveforms" section introduces the general traveling wave, supported by a book that does not mention the word wavelength at all, as far as I can tell. It also states without source that "Such waves occur in music and picture reproduction systems, in many digital circuits, in radio transmission and reception, and in waveguides," which is somewhere between untrue and misleading. I challenge you to find any source that indicates the concept of wavelength being applied to general waveforms in such systems. Dicklyon (talk) 14:33, 11 June 2009 (UTC)

The book is not cited as a reference to wavelength, but to the mathematical expression for the periodic form of the traveling wave. Brews ohare (talk) 14:40, 11 June 2009 (UTC)

Yes, I understand that. But you've added a bunch of complicating material to the wavelength article, when treatment of the concept of wavelength in sources seldom involves such complications. You've supported the complicating material by a book that doesn't even mention wavelength. Like I said when you first asked, the concept of wavelength is most often applied to sinusoidal waves, and if you want to say much about the more general case, you really ought to support that by something better than a throwaway line in a figure caption and such. That's why I found the book on ocean waves, where the shapes that propagate really are non-sinusoidal. Dicklyon (talk) 15:08, 11 June 2009 (UTC)

Hi Dick: It's great to be simple, but the subject has many ramifications, and it is not up to you to delimit what is too complex for inclusion. In fact, I'd argue that the general waveform is easier to understand than the sinusoidal one, and presents the connection of wavelength to velocity and frequency more transparently. I'd guess that you simply learned the material your way, and don't want to think it through in a different context.

The cited sources are much more than " throwaway lines", and if you disagree, provide some meat for your decisions, not arbitrary judgment calls. The source that "doesn't mention wavelength" was cited for the reasons mentioned above, which you apparently did not read.

For example, why cut the explained Wikilink to Fourier series, which connects the general and sinusoidal forms? Why cut the Wikilink to the cnoidal wave where a thorough discussion of an example of a periodic traveling wave is made? Why not provide your interpretation of the ocean wave source, which I read as saying the waveform is preserved because all components travel at the same speed? (In fact, how else can the waveform stay the same?) Brews ohare (talk) 15:42, 11 June 2009 (UTC)

Linking cnoidal wave would be OK, but the book source didn't mention wavelength anywhere need the discussion of the cnoidal wave. The "throwaway" I was referring to was in the caption of the figure 4.1 that you mention, where it says "complex waves, which nevertheless have distinct frequencies, or wavelengths." This ignores the fact that the usual "general" analysis, at least in linear systems, is in terms of sinusoids, since different frequencies typically have different velocities and there therefore the wave shape doesn't propagate unchanged. If you want to beef up the article, that's what really needs to be clarified, instead of pretending that the concept of wavelength is typically applied to complex waves. As for you "general case", please add it only if you find a source that connects it to the concept of wavelength. Dicklyon (talk) 19:25, 11 June 2009 (UTC)

You have re-inserted the errors about the ocean waves. This is not a linear system and does not propagate sinusoidal components. The notion of sinusoidal components is pretty irrelevant to how such a nonlinear system propagates wave shapes. Dicklyon (talk) 19:30, 11 June 2009 (UTC)

Ocean waves

Here is what the source Dicklyons introduced says about ocean waves:

"While maintaining this waveform, waves travel at a velocity determined by the wavelength. A wave number spectrum resulting from Fourier transform of this non-sinusoidal waveform contains not only the wave number corresponding to wavelength L, k_L = 2π/L, but also harmonic components such as 2πk_L, 3πk_L, and so on. From the fact that waves maintain their waveform during travel, it is understood that all of these wave number components travel at the same velocity as waves with wave number k_L.

Dicklyons deleted the following entry in the article that refers to these same waves and cites this same source:

In ocean waves the wavelength components all travel at the same velocity to maintain the shape of the waveform. This velocity is determined by the wavelength of the longest wavelength component.

with this supporting remark: "You have re-inserted the errors about the ocean waves. This is not a linear system and does not propagate sinusoidal components. The notion of sinusoidal components is pretty irrelevant to how such a nonlinear system propagates wave shapes."

Question 1: In what way does the meaning of the cited source depart from that of the reverted text? (My answer: in no significant manner.)

Question 2: Where does the topic of nonlinear systems appear outside of Dicklyon's comments? (My answer: the topic has never arisen in any text in the article.)

Question 3: Which is preferable: reinsertion of the brief and accurate reverted material, or an extended quotation from the cited source that says the same thing? Perhaps the reverted text should be slightly amended to refer to "ocean waves of large amplitude" to correspond more exactly to the source. Brews ohare (talk) 09:11, 14 June 2009 (UTC)

I think it's a matter of interpretation. In the ref, they take the fact that the non-sinusoidal wave propagates while maintaining its shape, and from that conclude that if you analyse it into Fourier components, then those have to all travel at the same speed. The way you wrote suggests the other way around, that the medium propagates components at the same speed, and hence the waveshape remains constant. However, if you were to look at the small-signal linear behavior, you'd see that different sinusoidal components do NOT propagate at the same speed, except in very shallow water. It's only the nonlinearity that makes them appear to synchronize their speeds. To describe such a nonlinear medium in terms of its propagation of sinusoidal components is nonsense. The topic of nonlinearity is appropriate here, because it's the only context (as far as I've found) in which it makes sense to talk about the wavelength of non-sinusoidal waves, instead of just sticking to sinusoids, which are the eigenwaves of linear systems. Dicklyon (talk) 17:16, 14 June 2009 (UTC)

Dick: Thanks for the reasoned response. The bottom line is that the various wavelengths travel at the same speed. The mechanism by which this result is made to occur may well involve some interesting aspects of nonlinear interactions, but the detailed explanation seems more than necessary here. I'd suggest that very little or no rewording of the reverted text is adequate.

I'll make a proposal in two or three days, when I've more time. Brews ohare (talk) 02:01, 15 June 2009 (UTC)

"The bottom line is that the various wavelengths travel at the same speed" is basically just your interpretation. There is only one wavelength involved – there is no periodic wave or wavelength associated with the harmonics. The fact that for the purpose of radar reflection these waves can be analyzed into different wavenumber components by a Fourier analysis is not a reason for us to state that different wavelengths propagate at the same speed, which is in fact very misleading. Dicklyon (talk) 02:17, 15 June 2009 (UTC)

Dick: Can you explain to me how your statement reconciles with your source that says: "In ocean waves the wavelength components all travel at the same velocity to maintain the shape of the waveform."? Brews ohare (talk) 16:22, 15 June 2009 (UTC)

Brews: the issue here, is that Fourier theory doesn't work in nonlinear systems. You just can't take a wave propagating in a nonlinear medium, decompose it into Fourier components, and talk about the propagation velocity of those components. The assumptions underlying Fourier theory fail in this case, and the velocities and components the math gives you have no basis in physical reality at all. Dick is essentially arguing that the source quoted above is incorrect. The wave propagates without changing shape, but this does not imply that there are actually sinusoidal components with different wavelengths, which propagate at the same speed. Checking the dispersion relation for the medium will immediately show that the latter cannot be the case.--Srleffler (talk) 04:45, 16 June 2009 (UTC)

What fails isn't the Fourier analysis, but the notion that the components are somehow separately treatable. The source was not incorrect in what it said, however; the paragraph at the top of p.263 deduces that components in a wavenumber spectrum propagate at the same speed from the fact that the wave maintains its shape; in that context, the wavenumber spectral decomposition is part of the radar reflection calculation, and he doesn't say anything about different wavelengths of the ocean wave itself; indeed, while a wavenumber spectrum makes some sense, a wavelength spectrum doesn't really, as the wave only repeats at the wavelength, not at submultiples of it. The source does not mention or suggest that there are wavelengths associated with the Fourier components, as that would not be a useful or very sensible notion in this context. One could argue that the wavenumbers correspond to wavelengths, but that source doesn't do that, for the reasons just stated, I think. Dicklyon (talk) 05:06, 16 June 2009 (UTC)

I see. So Brews is assuming incorrectly that where there is a wavenumber, there must be a wavelength.--Srleffler (talk) 05:22, 16 June 2009 (UTC)

I'm not saying that's necessarily incorrect, but it's certainly not appropriate here, and is not suggested by the source. Dicklyon (talk) 05:27, 16 June 2009 (UTC)

Reply to Srleffler

Statement by Srleffler: "Fourier theory doesn't work in nonlinear systems. You just can't take a wave propagating in a nonlinear medium, decompose it into Fourier components, and talk about the propagation velocity of those components."

This is an incorrect view. Fourier analysis is simply a mathematical decomposition that replaces a function with a sum of simpler functions, sinusoids for example. Being a mathematical procedure it does not rely upon any dynamics or physical theory, and is not predicated upon linearity. Thus, at each moment in time the waveform can be expressed by a sum of the basis functions, and if the waveform propagates rigidly, the basis functions also can be taken to so propagate, in which case the coefficients of the decomposition will be time independent. If you insist upon a full mathematical development of these facts, I will provide one. But my position is that you are confusing math with physics or vice versa. Brews ohare (talk) 01:45, 17 June 2009 (UTC)

I pretty much agree with that assessment, as I was explaining above, but providing a full development of Fourier theory won't do a thing to make the inclusion of your concepts in this article more acceptable. Dicklyon (talk) 02:36, 17 June 2009 (UTC)

I admit the error in describing the math, however waves are a physical entity and I insist that an article on them deal with physics, not math when the two depart from one another. The decomposition of a wave in a nonlinear medium into sinusoidal components is unphysical, in that those components do not propagate the same as an isolated wave with the same frequency would. --Srleffler (talk) 04:35, 17 June 2009 (UTC)

There is no need to arbitrarily insist on a particular description, or to forgo either physics or math on some general basis. If you would like to insist that a pure sinusoid would not propagate as a traveling wave, but would evolve into a sum of multiple sinusoids, that simple statement could be added with a suitable source for backup. Brews ohare (talk) 04:51, 17 June 2009 (UTC)

There is no need to develop Fourier series in the article; it was simply suggested FYI, in case there was disagreement. IMO acceptance of the above argument makes refusal to accept the reverted text a complete non sequitor. I will attempt to formulate that for you in an A -> B -> C fashion, if you like. Brews ohare (talk) 04:03, 17 June 2009 (UTC)

Reply to Dicklyon

Statement by Dicklyon: "the paragraph at the top of p.263 deduces that components in a wavenumber spectrum propagate at the same speed from the fact that the wave maintains its shape; in that context, the wavenumber spectral decomposition is part of the radar reflection calculation, and he doesn't say anything about different wavelengths of the ocean wave itself"

The belief that the source "doesn't say anything about different wavelengths" is an incorrect interpretation of the source. If a fixed shape waveform traveling in time is Fourier analyzed into a sum of basis functions that propagate at the same rate as the traveling wave, the decomposition coefficients are time independent. There is no requirement that the underlying physics or the medium be linear. The mathematical requirement is only that the the wave be a traveling wave. If the wave is a traveling periodic wave, as envisioned by the source, and a Fourier series in sinsusoids is used, the basis functions all will be harmonics of the fundamental. Each harmonic corresponds to a wavenumber, which simply is the analog in space of frequency in time. Your objections to the reverted text are thus based upon a misconception that there is physics involved here, where it is only math. Brews ohare (talk) 02:17, 17 June 2009 (UTC)

No, my objections to the reverted text are based on the fact that it is your own synthesis of concepts, not something you'll find in a source. Why are you pushing to include this strange text? Dicklyon (talk) 02:33, 17 June 2009 (UTC)

Dick: I am not synthesizing concepts; I am summarizing the source you provided. If you prefer, I will quote it at length directly, which will allow those who understand it to understand it, and those who don't to preserve their misconceptions. Brews ohare (talk) 04:03, 17 June 2009 (UTC)

My edit

The removal of "eigenfunction" was deliberate: Wavelength is a basic concept. This article should try to stay at a level where an intelligent 11 year old can understand it. Concepts like eigenfunctions should not be introduced so early in the article, if at all. I like the new wording, which gets the concept in there, but avoids the word.--Srleffler (talk) 04:51, 16 June 2009 (UTC)

Right, but you removed the reason why sine waves are used, which is that they are the unique shapes, in linear time-invariant systems, that propagate unchanged. So I added that in plainer language. Dicklyon (talk) 04:57, 16 June 2009 (UTC)

I wonder if the reason for using sinusoids is correctly identified. In the media you describe, I suspect that all wave shapes propagate unchanged, inasmuch as they are composed of sinusoids that themselves so propagate, provided only that the speed of propagation is independent of wavelength. Brews ohare (talk) 05:14, 17 June 2009 (UTC)

That would be true only in linear non-dispersive media; in water surface waves, waves of different wavelengths propagate at very different speeds, as one of the refs I pointed out shows. In nonlinear media, only certain shapes will propagate unchanged. Sinusoids are used in the case of linear media, dispersive or not, since the dispersion relation (between wavelength or wavenumber and velocity) completely determines how waves propagate. In nonlinear media, decomposing into sinusoids serves no such function; one might as well describe periodic waves in terms of Haar-function basis. To speak of sinusoidal components in nonlinear media really serves little purpose, in general. Dicklyon (talk) 06:08, 17 June 2009 (UTC)

What did you think was a reason for using sinusoids? Why are you pushing sinusoidal decomposition? Dicklyon (talk) 06:10, 17 June 2009 (UTC)

I'm pushing sinusoidal decomposition because it is the principal justification for treating sinusoids at all, which seems to be your primary topic. Brews ohare (talk) 14:42, 17 June 2009 (UTC)

That was a perfectly circular statement. And what are saying is my primary topic? Dicklyon (talk) 05:07, 18 June 2009 (UTC)

Language of discussion

Here is roughly how I'd approach the topic:

The simplest mathematical description of a traveling wave in one dimension is:

$y=f(x-vt)$

where y is the wave amplitude and f(x) is any function whatsoever. (Maybe some interpretation here, like: "a point x_t = x-vt moves with speed v, causing the position of the corresponding amplitude y = f(x_t) in the wave to travel with speed v"). If f(x + λ ) = f(x) for some λ, a wavelength may be defined and the traveling wave is called periodic. Under some rather general mathematical conditions, regardless of whether a wavelength can be defined:

$f(x)=\sum _{n=1}^{\infty }c_{n}\phi _{n}(x)\ ,$

where the set φ_n are referred to as basis functions. Using this decomposition, the traveling wave can be expressed as:

$y=\sum _{n=1}^{\infty }c_{n}\phi _{n}(x-vt)\ ,$

and each basis function φ travels at the wavespeed v. If the wave is periodic, the set φ_n can be chosen as sinusoidal waves, where the wavelength of each component wave is a multiple of that of the fundamental (longest wavelength) basis function and the basis functions often are called harmonics of the fundamental.

The application of this description to physical examples would follow. That might include a demo that the wave equation has such solutions, how that equation evolves in different contexts, and so forth. All depends upon how far one wishes to extend the simple idea of wavelength as expressed in f(x + λ) = f(x) into the subject of waves and wave equations (which is an extension, I'd say). Brews ohare (talk) 12:43, 17 June 2009 (UTC)

Pardon me if you already understand this, but this treatment works only for waves in a linear, dispersionless medium. In most media, y also has direct dependence on t:

$y=f(x-vt,t)$

This reflects the fact that the wave changes shape as it propagates. (Waves may also of course decay or have gain.) In a linear medium, you can describe how y evolves with time by considering a decomposition on a basis of sinusoidal waves with distinct velocities determined by the dispersion relation of the medium. Decomposing on a basis of sinusoidal waves that all propagate with the same velocity will not correctly describe the time evolution of the wave, in general.-Srleffler (talk) 03:56, 18 June 2009 (UTC)

Pardon me in turn, but this formulation is entirely mathematical. As such it stands on purely logical ground, and like all mathematics, may or may not have application to any particular physical situation. It simply is misguided to believe that math only works when there exists a physical application.

To stimulate some thought on your part, I challenge you to point out one place in the above math where linearity or lack of dispersion is invoked or is necessary without entering into a particular physical application. Brews ohare (talk) 09:29, 18 June 2009 (UTC)

I'm not arguing your math is wrong. I am arguing that you have chosen the wrong mathematical model for the physical system you seek to describe. The equation $y=f(x-vt)$ does not accurately describe wave propagation in real, physical media. It is a naive model, a lie-to-children. There are exceptional cases in which waves propagate without changing shape or amplitude, but these are rare special cases.--Srleffler (talk) 17:30, 18 June 2009 (UTC)

So simple cases are "lies to children"? We are talking wavelength here, and wave motion is mentioned mainly as illustration of wavelength. Simple cases are a good start. Brews ohare (talk) 19:09, 18 June 2009 (UTC)

As pointed out before, the decomposition into sinusoids is only useful for linear systems, such that the time evolution of the system can be described in terms of the time evolution of the components, added up; it works because sinusoids are special: they are the eigenfunctions of continuous-time linear systems (actually, complex exponentials are, but close enough). In the case of periodic non sinusoidal waves propagating, the linear system that will do that has to be pretty trivial, namely dispersionless, in which case the sinusoidal decomposition is hardly interesting or informative. And for real physical systems that will propagate waves without changing their shape, they tend to be nonlinear, in which case there is no longer any physical or mathematical motivation to consider sinusoidal analysis of the waves. Furthermore, even writing the general form of the traveling wave goes beyond what's needed to clearly explain the idea of wavelength, and no source that I've found couples that mathematical general form with the notion of wavelength. Without sources that couple these things, why would we put them into the article? Brews, you've even added "all the components travel at the same rate, which insures that the waveform remains unchanged as it moves," which is totally backward logic; you deduced the equal speeds of the components from the fact that the wave travels as a fixed shape, which is a trivial and useless result; you can turn it around and use it show that it "insures that the waveform remains unchanged as it moves"! Dicklyon (talk) 04:59, 18 June 2009 (UTC)

There is no validity to the claim you are making about "sinusoids are special" and about "eigenfunctions of continuous-time linear systems". The whole subject is simply one of a complete set of basis functions, which transcends any concept of eigenfunctions, although eigenfunctions (e.g. of a Sturm-Liouville equation) are included as special cases. How these basis functions propagate is determined by the mathematical form (e.g. f(x - vt)) not by physics.

Of course, in any particular application to a physical problem one has to ask whether the math is applicable.

Again, your viewpoint is based upon a physical situation. The math stands independently, and makes no presumptions about linearity. This is not a superposition of forces or excitations: it is a superposition of functions pure and simple. From a physical standpoint there are a number of examples where the math works. You have named linear systems, but you also have named some special cases of nonlinear systems where it also works. Whether math applies to a physical problem is not about math, it is about the physics. This formulation is math, pure and simple. Brews ohare (talk) 09:29, 18 June 2009 (UTC)

This is a physics article. If the math does not describe the physical systems under discussion, it is not suitable for inclusion in the article. --Srleffler (talk) 17:35, 18 June 2009 (UTC)

Sorry, Srleffler. There is no requirement that this be strictly a physics article. In fact, most physics articles contain quite a bit of math. The math is quite general and applies to many physical systems. It is not clear to me why the article should be restricted to "physical systems under discussion" where the math doesn't apply. That would eliminate the wave equation, for example. Brews ohare (talk) 19:07, 18 June 2009 (UTC)

Brews, it would be helpful if you would not keep adding such irrelevant and misleading stuff, against the consensus of other knowledgeable editors. Instead, maybe you can explain the point of it. How does it help to clarify the concept of wavelength to discuss mathematical decompositions of things that have wavelengths? Do you know any sources that do anything resembling that? Dicklyon (talk) 05:05, 18 June 2009 (UTC)

This "stuff" is neither misleading nor irrelevant; rather the shoe is on your foot. The logical exposition is to start with f(x-vt), move to a periodic traveling wave to define wavelength as f(x+λ-vt) = f(x-vt) = f(x-v(t+T)) -> λ = vT and then introduce a basis set and show the basis functions may have higher periodicity. Sine waves are introduced as a particular case. Your argument is that the general case is "irrelevant" because you can identify the phenomena in a special case (the sinusoid). That is like saying Shakespeare is irrelevant because all the elements are in Nancy Drew. Brews ohare (talk) 11:02, 18 June 2009 (UTC)

Who does it this way? What is the logical role of the basis decomposition here? I don't understand what you're saying about sinusoids here; why would this particular case be interesting or relevant? Dicklyon (talk) 14:11, 18 June 2009 (UTC)

I've broken the subject up into bite size pieces to make the relevance clear and added several references to the approach. I hope that it works now. Brews ohare (talk) 19:11, 18 June 2009 (UTC)

One source of relevance is to make connection to the notion of dispersion: a general waveform propagates unchanged only if its component parts can so propagate. To understand that, one has to introduce the notion of component parts. Brews ohare (talk) 19:41, 18 June 2009 (UTC)

The result remains nonsensical, since the idea of components propagating only makes sense in linear media. Your statement that "Such circumstances sometimes do occur in nonlinear media" is misleading, or downright wrong, if by "such circumstances" you mean "that the medium must be capable of propagating disturbances of different wavelengths at the same wave speed". Nonlinear media typically do NOT have that property, yet can propagate periodic non-sinusoidal signals (only of particular shapes, though -- they can't propagate sinusoids, for example, at non-trivial amplitude). Dicklyon (talk) 01:00, 19 June 2009 (UTC)

Furthermore, I still don't see your point. Why do you want to talk about a decomposition into sinusoids and/or other basis functions when it leads nowhere useful? Or what useful place do you think it leads? And what source connects this approach to the notion of wavelength? Neither of your new cited sources uses the word "wavelength" anywhere near the cited material. Dicklyon (talk) 01:03, 19 June 2009 (UTC)

Dick: How can the "result be nonsensical" when it is the most common case? Why does a supposed restriction to linear media disqualify this material from appearing, when linear media are the common examples at the beginning of all discussions of wave motion, and such waves exhibit wavelength just like more complex cases? Brews ohare (talk) 05:25, 19 June 2009 (UTC)

Have you understood nothing anyone else has written here? The material you keep pushing into the article is not the most common case. In nearly all media, general waves change shape as they propagate. General waves that propagate with a fixed shape are a very odd special case.--Srleffler (talk) 05:42, 19 June 2009 (UTC)

Srleffler: You are misreading what has been said. The statement was that most introductions to wave motion use the presented case and formalism. They also tend to use the simple wave equation and d'Alembert's formula. For example, didn't you learn wave motion first using the case of vibrations on a string? The limitations of the example are clearly stated along with Wiki links to more general cases. Brews ohare (talk) 05:54, 19 June 2009 (UTC)

Dick: How can occasional occurrence of "such circumstances" be either wrong or misleading when (i) there is a disclaimer that it is not the usual case, and (ii) two examples are cited and sourced, one due to yourself? Brews ohare (talk) 05:25, 19 June 2009 (UTC)

Dick: How is it that the presentation "leads nowhere useful" when at a minimum it leads to an understanding of why traveling waves are unusual and an understanding of what the implications of dispersion are? Brews ohare (talk) 05:25, 19 June 2009 (UTC)

Dick: Why should a connection with such other Wiki articles such as wave equation and d'Alembert equation be frowned upon. These topics are paramount in introductions to wave motion, and several are cited. The entire apparatus of generalized Fourier series had wave motion in linear media as its key motivating example. Why suppress this material and its connection? Brews ohare (talk) 05:25, 19 June 2009 (UTC)

Dick: I feel that you are way out on a limb here. Please attempt to provide some real objections to this well presented and well cited material. Your present objections seem to be either contradictory or wrong headed. Is this just a refusal to read what is there, or are you grinding axes I don't know about? I am reverting your edit and requesting an outside review. Brews ohare (talk) 05:25, 19 June 2009 (UTC)

I have to agree with Srleffler that you seem to be unwilling to listen to or understand the patient explanations of others. This is no surprise, really, as I've admonished you before to try not to provoke arguments by pushing your idiosyncratic points of view on several other articles already. Dicklyon (talk) 07:09, 19 June 2009 (UTC)

Sorry, Dick. I thought I was listening. I have rephrased the matter several times in the article, added figures to the article, and provided discussion here on the talk page that has not produced any detailed suggestions, but only personal attacks. It is nonsense that the entire mathematical formulation underlying dispersion that has been the subject of multiple monographs over centuries is an "idiosyncratic point of view ". (References cited in article.) That kind of criticism, which is simply intended to put me in my place and has no value in trying to fix things, is very common in your comments. Brews ohare (talk) 13:25, 19 June 2009 (UTC)

Is the section More general waveforms relevant?

A dispute has arisen in the article wavelength over the relevance of discussion of wavelength for general waveforms. This dispute has enveloped even rather trite matters, such as the caption of figures and the inclusion of figures.

(i) There is consensus that wavelength can be defined for general periodic traveling waveforms. However, the caption provided in the reverted version is under dispute, as is the reference cited to a figure that shows a similar waveform.

(ii) Objection is raised to use of the standard mathematical expression for a traveling wave, f(x - vt) despite references to sources that use this form, and despite links to other Wiki articles employing this form.

(iii) Objection is raised to presenting the standard Fourier expansion of such a general waveform, with Wiki links to appropriate articles and full citation of sources, with the intent of showing that a general waveform necessarily involves shorter wavelength components, and therefore places restrictions upon the dispersion of an allowed medium.

(iv) The proposal is made that only allusion to a simple example of surface water-waves should be provided, and all discussions bearing upon linear media be omitted, despite the fact that wavelength is a property of all waves regardless of their physical origin.

Please suggest whether you think this material is relevant to the article wavelength. Brews ohare (talk) 05:25, 19 June 2009 (UTC)

Amplification of point (iv)

A sub-section of More general waveforms contains this wording:

Thus, all the components must travel at the same rate to insure that the waveform remains unchanged as it moves. To turn this discussion upside down, because a general waveform may be viewed as a superposition of shorter wavelength basis functions, a requirement upon the physical medium propagating a traveling wave of fixed shape is that the medium must be capable of propagating disturbances of different wavelengths at the same wave speed. This requirement is met in many simple wave propagating mediums, but is not a general property of all media. More commonly, a medium has a non-linear dispersion relation connecting wavelength to frequency of oscillation, and the medium is dispersive, which means propagation of rigid waveforms is not possible in general, but requires very particular circumstances. Such circumstances sometimes do occur in nonlinear media. For example, in large-amplitude ocean waves, due to properties of the nonlinear surface-wave medium, wave shapes can propagate unchanged.^[10]

Dicklyon and Srleffler have deleted this discussion more than once, along with the supporting mathematical development, to leave only the last sentence on the surface wave example. Dicklyon has said, however, concerning this paragraph: "[the suggestion that] "Such circumstances sometimes do occur in nonlinear media" is misleading, or downright wrong, if by "such circumstances" you mean "that the medium must be capable of propagating disturbances of different wavelengths at the same wave speed". Nonlinear media typically do NOT have that property, yet can propagate periodic non-sinusoidal signals (only of particular shapes..." My view is that the existing wording has been misconstrued, and the discussion of dispersion is in fact entirely in agreement with Dicklyon's comment.

Comment is requested upon whether this paragraph is indeed misleading and how it might be re-phrased rather than deleted. Comment also is solicited as to inclusion of the supporting mathematical development outlining multi-wavelength components of a general waveform and its connection to dispersion. Brews ohare (talk) 13:18, 19 June 2009 (UTC)

Comments on RfC

I object to Brews's singular focus on presenting a general traveling wave decomposed on a basis of sinusoidal waves that propagate at the same velocity as the superposition. Sinusoidal waves in real media propagate at the phase velocities given by the medium's dispersion relation; in nearly all cases the velocity of such waves varies with their frequency. I have no objection in principle to presenting the idea that a general wave in a linear medium can be decomposed into a sum of sinusoidal waves, but the mathematical treatment Brews insists on is simply inappropriate, and its presentation is misleading in that it implies that in general waves can propagate without changing shape. The derivation is also long and only peripherally related to the topic of this article. The treatment of this topic in the article needs to be much briefer.

Brews's point (iv) above does not seem to me to accurately reflect the discussion above. I presume this is due to error or poor phrasing.--Srleffler (talk) 06:33, 19 June 2009 (UTC)

Response: The nature of dispersion is clarified by showing that a general waveform may be viewed as a superposition of shorter wavelength components. Hence, dispersive media cannot propagate rigid waveforms. There is no implication whatsoever in the article that propagation of rigid waveforms is a general phenomenon. Nonetheless, the formalism for linear media has a long history (going back earlier than d'Alembert's formula for solution to the wave equation), and there is no reason to exclude it from the article. Brews ohare (talk) 14:28, 19 June 2009 (UTC)

I'll comment on the numbered points, though my position is already clear in the record above, I think:

(i) The caption specifically referred to a figure in a reference for no apparent reason, so I took that out. Is that what there's a dispute about?

(ii) The standard mathematical expression for a traveling wave, simplified to one dimension, is not in itself a problem, but if we don't have any source that presents it in connection with the notion of wavelength, then it seems to be a gratuitous extra complicating bit of math that doesn't help at all to explain the topic.

(iii) Fourier expansion is not helpful or useful in explaining the notion of wavelength; see extensive discussions above.

(iv) I don't know what Brews is referring to here.

Dicklyon (talk) 07:04, 19 June 2009 (UTC)

Response: There are numerous sources cited to support the notion that a general waveform is made up of shorter wavelength components. A figure is added to show a saw-tooth example. This fact is important to the understanding of why a rigid waveform cannot propagate unchanged unless different wavelengths all propagate at the same wave speed. I believe that provides a connection of the math to the topic of wavelength. Brews ohare (talk) 14:28, 19 June 2009 (UTC)

It would indeed make sense to say something about why non-sinusoidal waves usually do not propagate as an unchanging shape in typical linear systems; that discussion belongs in the section on sinusoids, which are the eigenfunctions that such systems propagate, and it should only take a few lines. That's why the concept of wavelength is most often applied only to sinusoids, and whey the "general case" is such a rare special case. There's no need to this long-winded approach in the section where the result it essentially in applicable. Dicklyon (talk) 14:59, 19 June 2009 (UTC)

Perhaps what we have here is a well-known aspect of pedagogy: some minds like to work from the concrete example to its generalization, while others work better beginning from the general case and specializing to particular examples. Brews ohare (talk) 16:49, 19 June 2009 (UTC)

You haven't presented a "general case". A wave that propagates with unchanging shape is not at all "general". Pedegogically, it is often good to start with a naive model like the one you have presented, and then move to more sophisticated models as needed. In this case, though, I don't see the need for the mathematical derivation at all. A few lines of text would suffice to explain that general waves can be decomposed into sine waves; the details can be left to other articles. With this approach, it is no longer necessary to use a naive model in which there is no dispersion. --Srleffler (talk) 18:11, 19 June 2009 (UTC)

Response: The case is not general from the point of view of a "general physical medium". It's general in the sense of not being restricted to a single sine wave, but allows for (i) general basis functions and (ii) more than one basis function. It also extrapolates to two and three dimensions with little change. Brews ohare (talk) 22:51, 19 June 2009 (UTC)

Objection

How are we to have a proper RfC when you, Dicklyon, remove the version under discussion and replace it with the version that you and Srleffer wish to see instituted. What do you think the RfC is for anyway? Do you expect a commentator to retrieve the version under discussion from the history page? This behavior is worthy af a call for censure. Brews ohare (talk) 07:32, 20 June 2009 (UTC)

Comments on amplified point (iv)

The objections have been explained, and are unrelated to your funny claim that "all discussions bearing upon linear media be omitted". Dicklyon (talk) 22:10, 19 June 2009 (UTC)

Response: I've quoted your objections in the #Amplification of point (iv), which indicate you have not read the paragraph in this amplification. You prefer now not to address the issues, but to digress into something called vaguely "funny claims". Try to be helpful and not just to ping-pong. Brews ohare (talk) 22:37, 19 June 2009 (UTC)

A "rare special case"

Maybe the approach is not so uncommon. See examples of use of the d'Alembert formula & Fourier analysis and dispersion. Brews ohare (talk) 15:58, 19 June 2009 (UTC)

I don't think that's at issue. I'll wait to do more on this until I see if anyone will support your approach via the RfC you called. Dicklyon (talk) 18:01, 19 June 2009 (UTC)

Beat wave

Amplitude modulated waveform

First three terms in Fourier expansion of sawtooth

The new figure is also quite misleading, as the concept of "wavelength" would never be applied to a beat wave of that shape, as far as I've ever seen; more likely the wavelength associated with that figure would be the shorter length that's apparent. Dicklyon (talk) 17:56, 19 June 2009 (UTC)

Can you flesh out that view? The wave actually does not repeat with the shorter wavelength of its constituents. As a counterexample, if only the first few harmonics of the sawtooth were summed, an apparent small scale ripple effect would not lead one to think the wavelength of the sawtooth were the wavelength of the ripple. Continuity of interpretation would suggest the same holds true for the beat wave. Is this a topic worthy of more discussion in wavelength? Brews ohare (talk) 19:30, 19 June 2009 (UTC)

Consider an AM radio (medium-wave or short-wave) signal. These signals have their wavelengths conventionally described in terms of he carrier wavelength, even though the signals are not exactly periodic. If you AM modulate with a sine, it is not conventional to describe the wavelength as the much longer distance of which the signal is exactly periodic. It would be better to stick to the conventional application of the terminology, which does not even require exact periodicity, and which makes your whole treatment irrelevant, in addition to be being unsourced. Dicklyon (talk) 21:43, 19 June 2009 (UTC)

Dick: Have you a source for the practice in AM modulation for deciding wavelength? I can understand talking about the carrier wavelength in this application because the modulation is a signal of variable content, and doesn't characterize the waveform unless the envelope itself is periodic. Is there anything more to it? Brews ohare (talk) 22:20, 19 June 2009 (UTC)

A related example occurs in calculating energy bands in solids, where the high frequency oscillations (the carrier) is ignored (it relates only to the inner electrons at the atomic core) and the real information is contained in the long wavelength parts of the wave function. This case is similar to the radio case where the carrier has no information and the modulation has it all. So from the information standpoint, one wants to characterize the envelope not the carrier. Brews ohare (talk) 22:43, 19 June 2009 (UTC)

Are you saying you don't know or agree that the wavelength of radio signals is based on the carrier? Or you just want me to find some sources for you? The same is true by the way for the modulated light in wavelength-division multiplexing. If you'd look at sources instead of making up a story based on intuition and logic, we'd have an easier time here. Dicklyon (talk) 03:38, 20 June 2009 (UTC)

I asked you directly for sources. It is not hard to understand. You have provided none. Brews ohare (talk) 07:34, 20 June 2009 (UTC)

Another common definition, "The distance between successive crests of a wave", avoids a lot of this confusion. It is the definition generally used for sinusoids and locally sine-like waves, including modulated ones. More such are here, or these books. It makes the whole concept of Fourier decomposition more obviously irrelevant to the topic. So let's take it out. Dicklyon (talk) 04:11, 20 June 2009 (UTC)

I'm glad the confusion is resolved, although I'm not clear exactly which confusion. This is exactly the definition used in the above two figures I provided you of a modulated wave and of a sawtooth wave. The term "successive crests" may refer to two successive global crests (that is, crests of the envelope), or to two successive minor internal crests that are only local maxima and determine what often is called the local wavelength. The distribution of local wavelengths is determined by both the carrier and by the envelope. (It's a wavepacket.) Brews ohare (talk) 07:36, 20 June 2009 (UTC)

Have you found an example where the interpretation is these so-called "global crests" in the context of a waveform that has internal crests? Dicklyon (talk) 15:41, 20 June 2009 (UTC)

A couple comments on the issues in this section: note that one can produce a beat wave much like the figure above, by beating together two waves with closely-spaced frequencies f₁ and f₂, in a linear medium. The result is a wave with short-period oscillations and a longer-period envelope with frequency equal to f₁ - f₂. Brews might be tempted to talk about the "global wavelength" obtained by measuring from one crest of the envelope to the next, but note that if the medium is linear there is no Fourier component with this frequency or the corresponding wavelength. The only two components present are the original f₁ and f₂. (Radio modulation of course involves nonlinear effects, so this is not the case there.)

Also note that a modulated wave or beat wave does not necessarily exactly repeat on each cycle of the envelope. The waveform only exactly repeats on each cycle if the spatial period of the modulation is an integer multiple of the carrier wavelength. If the ratio is irrational, the waveform never exactly repeats.

My point is that attempting to assign a "wavelength" based on the envelope of a waveform, or based on absolute repetition, is likely to lead to treatments that aren't rigorous. --Srleffler (talk) 06:16, 23 June 2009 (UTC)

New definition proposal

One wave packet in a possible train of wave packets

I think that if we start with the common and easily sourced definition of wavelength being the distance between successive peaks or troughs of a wave (this is the one in the cited first ref already), we can fix the article and avoid the temptation to add all the idiosyncratic complexity that the article has accumulated in the last week or so. But before I do that, I'll ask here: what other good sourced definitions are there that we need to also include? Dicklyon (talk) 04:38, 20 June 2009 (UTC)

In case you did not notice, this definition is provided in the figure caption in the first figure of the disputed section. It has two possible interpretations: one involving local crests and determining the local wavelength, and the other involving the separation of global crests (crests of the envelope). Are you suggesting introduction of the notions of wave packets and the distribution of local wavelengths across a wave packet? See Goldston or Bromley for example. Brews ohare (talk) 07:27, 20 June 2009 (UTC)

BTW, before embarking upon a total revision that undoubtedly will lead to much "discussion", and that will make the RfC impossible as there is nothing to comment on (it all having been removed by yourself unilaterally) how about waiting a little to see if anything comes from the RfC? Brews ohare (talk) 09:07, 20 June 2009 (UTC)

Yes, that figure clued me in that your interpretation of wavelength included a rather atypical definition, and thought we should consider refocusing on the standard definition. Neither of the books you link above include the term "local wavelength". Dicklyon (talk) 15:40, 20 June 2009 (UTC)

Local wavelength

Brews, what is this new concept of local wavelength that you've introduced with no supporting source? I can't find anything on it, so I'll take it out until we have a source we can work from. Dicklyon (talk) 15:24, 20 June 2009 (UTC)

Dick: Well I'm sorry that your resourcefulness in using Google has reached such a low ebb, along with your sense of responsibility and restraint. I have provided one such source: there are dozens. Brews ohare (talk) 16:14, 20 June 2009 (UTC)

But the source you provided doesn't treat "local wavelength" as a different concept from the general definition of wavelength, and doesn't imply the existence of a "global wavelength", which is the distinction you're trying to support with it. Dicklyon (talk) 18:21, 20 June 2009 (UTC)

And you've still got the statement "a narrow range of wavelengths is necessary to produce a localized wave packet, and the more localized the envelope, the larger the spread in required wavelengths. In effect, the envelope of the wave form modulating the carrier wave (the high frequency internal wave motion) introduces a distribution of local wave lengths in the vicinity of the wavelength of the carrier," which in flatly contradicted by the sourced definition, at least in the case of AM modulation and Gaussian-enveloped sine waves. Dicklyon (talk) 18:24, 20 June 2009 (UTC)

Hi Dick: Sorry, you are wrong about this and the sources don't support you. Try making some quotes to illustrate your views, instead of pronouncements from your elevated knowledge of all subjects. For example the statement:

"a narrow range of wavelengths is necessary to produce a localized wave packet, and the more localized the envelope, the larger the spread in required wavelengths."

may be compared with:

"The amplitude of the Fourier transform of a Gaussian function is itself another Gaussian function centered at a frequency of zero. Its width on the frequency axis is inversely proportional to the width of the original Gaussian function. Graham

I hope you can make the translation from time and frequency to position and wave vector.

I am quite confident that you know all this stuff, you are just being obstructive and destructive. Brews ohare (talk) 18:35, 20 June 2009 (UTC)

Comment: "Local wavelength" certainly seems to be a commonly used term: "local wavelength" a search for "local wavelength" on Google Scholar gives 1,320 hits. I'll investigate further. -- The Anome (talk) 18:40, 20 June 2009 (UTC)

Yes, it's a term sometimes used, and I don't mind incorporating anything that a source says about it. But Brews is using it inappropriately to synthesize other concepts that he wants to talk about that are not sourced. For example, he has now added "In the case of carrier modulation (the carrier is the high frequency internal wave motion), the envelope of the wave form modulating the carrier wave introduces a distribution of local wave lengths in the vicinity of the wavelength of the carrier," backed up by two sources, neither of which mentions "local wavelength" nor even "wavelength" anywhere near the cited pages. Dicklyon (talk) 19:57, 20 June 2009 (UTC)

Several more erroneous interpretations are manifest in "In representing the wave function of a particle, the wave packet is often taken to have a Gaussian distribution of wavelengths and is called a Gaussian wave packet. It is well known from the theory of Fourier analysis, or from the Heisenberg uncertainty principle (in the case of quantum mechanics) that a narrow range of wavelengths is necessary to produce a localized wave packet, and the more localized the envelope, the larger the spread in required wavelengths." The cited refs and linked article do NOT support these statements. Brews instead on connecting wavelength to spectral analysis concepts, which is mostly inappropriate, and certainly unsourced and WP:SYN at best. Dicklyon (talk) 20:08, 20 June 2009 (UTC)

Hi Dick: Just what do you think the sources say? A definition of local wavelength is referenced to Cooper, and is exactly the one stated in the article. The other sources indicate a number of wavelengths are introduced by modulation. Is it necessary to have one source say everything word for word? A normal human can get the picture. Brews ohare (talk) 20:04, 20 June 2009 (UTC)

They say a lot of good and true stuff, but they don't connect it to the concept of wavelength as you are trying to do. The definition is fine. Show me where the other sources says that a number of wavelengths are introduce by modulation; I search near the pages you linked for wavelength, and didn't see that. Word for word is not the issue; your idiosyncratic interpretation is the issue. Dicklyon (talk) 20:08, 20 June 2009 (UTC)

I've cited O'Reilly & Russ. I'm sure you know that modulation of the carrier by a sine wave leads to sum and difference frequencies. A more complex modulation can be viewed as modulation by a superposition of sine-wave modulators, and so produces a bunched set of frequencies. Are you going to argue with me that these frequencies don't relate to a variety of wavelengths? Brews ohare (talk) 22:12, 20 June 2009 (UTC)

Yes of course I know about sidebands and sum and difference frequencies. But they are pretty much unrelated to wavelength. The sidebands of an AM modulated tone, in particular, leave the wavelength steady and unaffected, equal to the wavelength of the carrier. To try to apply these spectral decomposition techniques to wavelength is exactly what the problem is with your idiosyncratic approach. So yes, I do continue to argue that these frequencies don't relate to a variety of wavelengths. Do you have a source that suggests that they do? Dicklyon (talk) 23:40, 20 June 2009 (UTC)

Repeated deletion of material set up for Request for Comment

Dick: You insist on deletion of the material set up for request for comment, making any such comment impossible to achieve. That does not seem to me to be helpful in improving this section. Please desist and re-install this sub-section. Brews ohare (talk) 19:26, 20 June 2009 (UTC)

For your convenience, here is the sub-section for installation:

Thanks for putting it here, so we can discuss it without leaving this erroneous and misleading complicated mess in the article. Dicklyon (talk) 19:59, 20 June 2009 (UTC)

Great, go ahead and discuss. Your comments on the RfC already have been dealt with. That is why it would be nice to have this material where someone else could comment upon it. Brews ohare (talk) 20:07, 20 June 2009 (UTC)

If you can find someone to support your idea that this stuff is relevant, we can talk. My comments about why it is a combination of irrelevant expansion about waves and a strange unsourced interpretation of wavelength remains unrefuted, as far as I can tell.

There is nothing strange or unsourced about the the interpretation of wavelength as the distance between successive maxima or minima in a periodic waveform. What are you talking about, please? Brews ohare (talk) 20:33, 20 June 2009 (UTC)

For starters, can you show us a single source in which the notion of "wavelength" is discussed in the context of a periodic wave with intervening peaks between the corresponding points on the wave. If we had such a source to start from, it might provide a reasonable basis for what kinds of ways the notion of wavelength is applied in such contexts. Dicklyon (talk) 20:11, 20 June 2009 (UTC)

If wavelength refers to the distance over which the wave repeats itself, whether there is intervening structure of any kind is not pertinent. That wavelength must satisfy f(x+λ) = f(x) for all x. Alternative definitions of wavelength, local wavelength (google it), apply in a limited region of a waveform, and do not require periodicity at all. Do you argue that these different things do not both exist? Brews ohare (talk) 20:33, 20 June 2009 (UTC)

And what's all that stuff about solitons for? The wave form given there doesn't even have a wavelength! Dicklyon (talk) 20:17, 20 June 2009 (UTC)

The solitons come up only as an example of the propagation of a rigid waveform. This is apart from wavelength in the global sense, but has bearing in the local sense because the concept of a rigid wave as a superposition of shorter wavelength parts illustrates the need for propagation of all the parts at the same speed despite their different wavelengths. Brews ohare (talk) 20:33, 20 June 2009 (UTC)

You understand all these points, and are simply playing ping-pong. Brews ohare (talk) 20:33, 20 June 2009 (UTC)

I understand about solitons except for why you would add them to the article on wavelength. And as to whether "there is intervening structure of any kind is not pertinent," that seems to be worth investigating more. Why are you adding so much stuff to try to distinguish this case from the usual case if it's not pertinent? Dicklyon (talk) 20:47, 20 June 2009 (UTC)

RfC: Should the classic analysis of waveforms and wavelength be included in article Wavefunction?

The sub-section below is proposed to replace the present subsection of the same name in Wavelength. Comments are solicited on the advisability of its inclusion and any emendations that would improve it. Brews ohare (talk) 20:56, 20 June 2009 (UTC)

Please add comments here

• Quick note; the "Traveling periodic wave" image should not be used as is. Its red dot is unexplained/unexplainable, and shouldn't be there. Binksternet (talk) 21:03, 20 June 2009 (UTC)

Here is the subsection:

More general waveforms

See also: Wave

Wavelength of an irregular periodic waveform f(x − vt) = f(x + λ − vt) at a particular moment in time; the same wavelength marks the distance between similar positions in the waveform, for example, the distance between peaks and the distance between troughs.

The figure shows a wave in space in one dimension at a particular time. A wave with a fixed shape but moving in space is called a traveling wave. If the shape repeats itself in space, it is also a periodic wave. To an observer at a fixed location, the amplitude of a traveling periodic wave will appear to vary in time, and if its velocity is constant, will repeat itself with a certain period, say T. Assuming one dimension, the wave thus recurs with a frequency, say f, given by:

$f={\frac {1}{T}}\ .$

Every period, one wavelength of the wave passes the observer, showing the velocity of the wave, say v, to be related to the frequency by:

$v={\frac {\lambda }{T}}=\lambda f\ ,$

which implies the wavelength is related to frequency as:

$\lambda ={\frac {v}{f}}\ .$

Therefore, the results presented above for the sinusoidal wave apply to general waveforms as well.

Formal description

Traveling periodic wave; wavelength is the distance between green dots

In one dimension, a traveling wave that propagates without changing shape is described by the equation

$y=f(x-vt)\ ,$

where f is an arbitrary function of its argument, y = wave amplitude, v = wave speed or velocity, x = position in the wave, and t = time. If we define a particular value of the argument, say x_t given by:

$x_{t}=x-vt\ ,$

then a fixed value of x_t is located at a position x that travels in time with a speed v, which means the point in the wave with amplitude y = f (x_t) also travels in time with speed v.

To possess a wavelength the waveform must be periodic, which requires f(x) to be a periodic function. That is, f(x) is restricted to functions such that:

$f(x+\lambda -vt)=f(x-vt)=f(x-v(t+T))\ ,$

which recaptures the relation between wavelength and wave speed found intuitively above: λ = vT.

Connection to sinusoidal waves: components with many wavelengths

Superposition of sinusoidal wave basis functions (bottom) to form a sawtooth wave (top); the basis functions have wavelengths λ/n (n=integer) shorter than the wavelength λ of the sawtooth itself (except for n=1). All basis functions have nodes at the nodes of the sawtooth, but all but the fundamental have additional nodes. The oscillation about the sawtooth is called the Gibbs phenomenon.

Under rather general conditions, a function f(x) can be expressed as a sum of basis functions {φ_n(x)} in the form:

$f(x)=\sum _{n=1}^{\infty }c_{n}\varphi _{n}(x)\ ,$

known variously as Fourier series, Fourier-Bessel series, generalized Fourier series, and so forth, depending upon the basis used.

For a periodic function f with spatial periodicity λ, the basis functions satisfy φ_n(x + λ) = φ_n(x). This condition can be satisfied by basis functions that repeat more often in space than does f itself, and so have wavelengths shorter than the function f.

In particular, for such a periodic function f , the basis may be chosen as a set of sinusoidal functions, selected with wavelengths λ/n (n an integer) to ensure φ_n(x + λ) = φ_n(x). For a sine wave sin(kx) the implication is kλ = 2nπ (n an integer), or k = 2πn/λ, where k is called the wave vector and n is called the wavenumber. The wavelength of sin(kx) = sin(2πn x /λ) is λ/n. In this case, the basis function with wavelength λ is referred to as the fundamental and the other basis functions as harmonics. Many examples of such representations are found in books on Fourier series. For example, application to a number of sawtooth waves is presented by Puckette.

Whatever the basis functions, the wave becomes:

$y=f(x-vt)=\sum _{n=1}^{\infty }c_{n}\varphi _{n}(x-vt)\ .$

Thus, all the components must travel at the same rate to insure that the waveform remains unchanged as it moves. To turn this discussion upside down, because a general waveform may be viewed as a superposition of shorter wavelength basis functions, a requirement upon the physical medium propagating a traveling wave of fixed shape is that the medium must be capable of propagating disturbances of different wavelengths at the same wave speed. This requirement is met in many simple wave propagating mediums, but is not a general property of all media. More commonly, a medium has a non-linear dispersion relation connecting wave vector to frequency of oscillation, and the medium is dispersive, which means propagation of rigid waveforms is not possible in general, but requires very particular circumstances.

Such circumstances sometimes do occur in nonlinear media. For example, in large-amplitude ocean waves, due to properties of the nonlinear surface-wave medium, wave shapes can propagate unchanged. A related phenomenon is the cnoidal wave, a periodic traveling wave named because it is described by the Jacobian elliptic function of m-th order, usually denoted as cn (x; m). Another is the wave motion in an inviscid incompressible fluid, where the wave shape is given by:

$y=A\ \mathrm {sech} ^{2}[\beta (x-vt)]\ ,$

one of the early solutions to the Korteweg–de Vries equation of 1895. Here β is a constant related to height of the wave and depth of the water. The Korteweg-de Vries equation is an exactly solvable model, that is, a non-linear partial differential equation whose solutions can be exactly and precisely specified. The solutions include examples of solitons, traveling waves without a wavelength because they are not periodically recurring, but still capable of representation as sums of functions with definite wavelengths using the Fourier integral.

References

Brews ohare (talk) 02:56, 2 July 2009 (UTC)

The crux of the problem

As Srleffler and I have pointed out to Brews repeatedly, it is unconventional and quite pointless to tightly connect the notion of wavelength with the notion of spectral decomposition. The concepts are mostly incompatible, and the connection is mostly unsourced, not withstanding a few sources that mention that complex waves can be thought of as having components of different wavelengths. It is much more useful to connect the concept of wavenumber with spectral decomposition, since wavenumber is a frequency and its definition doesn't involve waveform features. The waveform features involved in defining wavelength, successive peaks or troughs or nodes or whatever, don't really generalize well to complex waveforms, and Brews's attempts to synthesize such a connection keep leading to demonstrably false statements, misleading statements, unusual idiosyncratic statements, etc. If we would just stick to what's sourced in connection with wavelength, it wouldn't be a problem.

As for local wavelength, that's worth talking about. It's just a recognition that the usual definition of wavelength may lead to results that vary, e.g. in nonuniform media. It's nothing to do with spectral decomposition, at least in the sources I've examined, which his how Brews keeps misapplying it.

I really don't understand at all why Brews wants to turn the wavelength article into an article on Fourier transforms, but he is clearly way out of his element in terms of understanding either, and should slow down, learn, and reduce the level of disruptive expansion here. Dicklyon (talk) 20:28, 20 June 2009 (UTC)

Response: The subsection contains a good deal more than the sub-sub-section Connection to sinusoidal waves: components with many wavelengths referred to in the first sentence. To suggest that wave number is the way to go is a bit silly considering the close connection to wavelength. On that basis there would be only one of the articles Wave number, Wavelength, or Wave vector. The statement that the proposed subsection is unsourced "not withstanding a few sources" is erroneous and inflammatory, and the characterization as containing "demonstrably false statements, misleading statements, unusual idiosyncratic statements" is simply name calling without constructive comment or validity. Brews ohare (talk) 21:11, 20 June 2009 (UTC)

The incorrect, misleading, and idiosyncratic items that you have inserted have been individually identified in numerous comments above. I'm not sure what your remarks about wavenumber mean here, as they seem to be disconnected from my comments about that. The point is that wavenumber is a frequency-domain concept, and that a lot of what you've been adding makes some sense with respect to wavenumber, and indeed many of the pages you cite refer to wavenumber and not wavelength. Wavelength is not a frequency-domain concept, and to try to apply those Fourier concepts to it, unlike what all the sources do, keeps leading you into these errors. Dicklyon (talk) 23:36, 20 June 2009 (UTC)

Brews seems to have completely missed Dick's point here: wavenumbers are not wavelengths. Wavenumbers are measures of frequency. This confusion has been part of the problem all along. Brews sees sources that discuss wavenumbers, and assumes that this is equivalent to discussing wavelengths, so he misinterprets the sources.--Srleffler (talk) 02:58, 21 June 2009 (UTC)

Right, spatial frequency that is. And while wavenumber and wavelength are 1:1 related for sinusoids, the frequency dimension of a Fourier decomposition is always the frequency (wavenumber), since wavelength makes much less sense there. And spectral decomposition by wavenumber is a concept that's generally useful, esp. in linear systems, but decomposition by wavelengths is not so useful, and seldom done. To turn the article on wavelength into an article on Fourier decomposition of complex waveforms is not motivated by any reliable source, as far as I can tell. Dicklyon (talk) 03:26, 21 June 2009 (UTC)

Due to having reverted Brews's nonsense 3 time today already, I can't do so again. I just noticed he's added yet another source on quantum mechanics with gaussian wave packets and such; all good stuff, but irrelevant, as it doesn't mention the concept of wavelength, much less local wavelength, which is the concept that he is trying to make verifiable. Dicklyon (talk) 23:43, 20 June 2009 (UTC)

I'm not finding any particularly clear definitions of "local wavelength", though there is this, which seems to be somewhat different than what Brews is talking about. Brews: I think the main question here is, would someone looking for an overview of the concept of "wavelength" really find this in-depth explanation about fourier series and quantum mechanics at all useful, or would it be better placed on another page? Perhaps the page about wave packets? —jacobolus (t) 00:16, 21 June 2009 (UTC)

Indeed, that book's use of local wavelength for the wavelength of an approximate sinusoid in a spatially varying medium, that is, the basis of the WKB or Liouville–Green approach, is how I've seen it used. It's not at all the way Brews is using it. And the question isn't just whether Brews's content is most useful here, but whether it's even correct, when he inappropriately remaps Fourier spectral stuff into wavelength; for example, a wave packet that's gaussian in space and in wavenumber is not gaussian in wavelength, even if you take the mapping of every Fourier component to a component parameterized by wavelength, which is not at all something that is normally done. Dicklyon (talk) 00:26, 21 June 2009 (UTC)

Here are some sources that might help you guys understand that I'm not ignorant if this area; some of the papers are available at my site dicklyon.com. Dicklyon (talk) 01:00, 21 June 2009 (UTC)

Dick: You say "Wavelength is not a frequency-domain concept, and to try to apply those Fourier concepts to it, unlike what all the sources do, keeps leading you into these errors." Of course the errors you refer to are not identified, so this comment cannot be addressed completely in this regard. However, the idea that wavelength is not a frequency domain concept is neither mentioned nor endorsed by anything I've seen, and you have not pointed out where this issue arises. There is an analogy, of course, between Fourier transforms in time and frequency, and Fourier transforms in space and wave vector, and as wave vector and wavelength are connected by the relation k = 2π / λ, it is clear that statements about k can be easily translated into statements about λ. I thought you knew all that Dick. Brews ohare (talk) 06:07, 21 June 2009 (UTC)

Yes, I have agreed that I know all that, except for that last bit that "statements about k can be easily translated into statements about λ" which is not as generally true as you'd like. Let me find you some links to errors I pointed out... Dicklyon (talk) 06:15, 21 June 2009 (UTC)

Here's one that doesn't so much depend on the difference between wavenumber and wavelength, but involves erroneous reasoning about Fourier components of a wave. Here's another that I thought would make it very clear to you that the wavenumber spectrum has little to do with wavelength; yet you just came back with more incorrect synthesis. Here is another, based on not understanding the relationship between wavenumber and wavelength again. Brews, as a wikipedia editor I never invoke personal credentials, since everything should be based on sources; but realize that I really do understand all this stuff, and you obviously don't; you've refused to base your edits on sources, choosing instead to support your ideosyncratic additions with references to sources that don't even mention the word wavelength in most case. This needs to stop. If you'd give us some clue about where you're coming from, maybe we could find a better way to help; if you're a student trying to learn, say so (this seems more likely than that you're an older guy, since you seem to be clueless about radio). Dicklyon (talk) 06:34, 21 June 2009 (UTC)

Suggestions for improvement and expansion of the article, June 2009

(suggested by Brews ohare, signed once after the last one)

Formal definition of wavelength

The present definition: "In physics, wavelength is the distance between repeating units of a waveform." is inadequate to cover the various uses of the term.

For example, in the case of an irregular periodic waveform, the definition is consistent with what one would expect, illustrated by the two measures of wavelength shown in the figure under More general waveforms.

However, wavelength also is used in non-periodic waves, perhaps as the distance between adjacent crests or troughs, or perhaps as a derivative of some wave property as in the WKB approximation, or in the discussion of action S.

The definition should be fixed to be more general and the article should be expanded to include a wider range of examples. Brews ohare (talk) 17:14, 22 June 2009 (UTC)

I agree that the present definition is not very good. We should replace or expand it, but only if the new version is directly supported by a reliable source. I'm not sure a wide range of examples is needed, but it probably depends on the examples.--Srleffler (talk) 05:53, 23 June 2009 (UTC)

It's true that one could define an instantaneous local wavelength in the WKB method in terms of the local wavenumber k(ω, t); I found a couple of sources that do so, and added Wavelength#Nonuniform_media. As for being "consistent with what one would expect", I think that's a personal criterion that has proved to lead us into errors in the past, and should be superceded by sources. Dicklyon (talk) 06:26, 23 June 2009 (UTC)

Yes, but it is the other way around: the wave number vector is defined as the gradient of the wave phase, and subsequently it is assumed in the L-G, WKB, or multiple-scales method that the wave number is slowly varying. The reference to start with is Whitham "Linear and nonlinear waves". -- Crowsnest (talk) 15:09, 23 June 2009 (UTC)

Right, it is as you say, and that's the book I have on my shelf that I originally learned this stuff from. Occasionally, though, some authors connect that to wavelength, so I added that connection as Brews requested. Is it OK? Dicklyon (talk) 15:51, 23 June 2009 (UTC)

Traveling waves

The article lacks any discussion of a wide body of literature and methods. Notably the formal definition of a traveling wave introduced as solutions to the wave equation by d'Alembert:

$y=f(x-vt)+g(x+vt)\ ,$

is not included, despite the fact that almost all discussion of wave motion begin with vibrations on a string, and introduce the various relations between wavelength, frequency and wave speed in this context. Brews ohare (talk) 17:18, 22 June 2009 (UTC)

It seldom shows up in discussion of wavelength; do you know any sources? For one thing, it's too narrow, eliminating all waves that change as they propagate, even those that have a well-defined wavelength. Dicklyon (talk) 06:26, 23 June 2009 (UTC)

Fourier analysis

The connection between wave length and spectral analysis of waveforms is lacking in this article. It is not possible to understand dispersion without it (as an example), nor the notion of wave packets and their relation to wavelength distribution. Brews ohare (talk) 17:21, 22 June 2009 (UTC)

Sources? Wavelength is not generally used in discussing Fourier analysis; wavenumber is the more appropriate concept. Dicklyon (talk) 06:26, 23 June 2009 (UTC)

Wave vector and wave number

The connection of wavelength to wave number and wave vector requires more attention in this article. At a minimum, examples should be present that show how these concepts may be interchanged in describing various waveforms. Brews ohare (talk) 17:23, 22 June 2009 (UTC)

For sinusoids, the relationship is simple; it's not clear where to go with that. For non-sinusoids, there's no useful relationship that I know of. If you have a source for what you have in mind, let us know. Dicklyon (talk) 06:26, 23 June 2009 (UTC)

Modulated waves

The wavelength in a modulated wave, which is not necessarily a periodically recurring waveform, needs elucidation. In particular, some discussion could be provided of how the envelope of such a wave introduces a range of wavelengths about the carrier frequency, in somewhat the same way as occurs in wave packet descriptions of particles in quantum mechanics, as subsumed under the Heisenberg uncertainty principle. Brews ohare (talk) 17:26, 22 June 2009 (UTC)

An AM modulated signal or a gaussian wave packet (gaussian envelope modulating an underlying fixed-wavelength carrier) has a constant wavelength, so there's not much to say. The idea of spectral analysis of such waves should be done in an article on frequency domain or wavenumber or Fourier analysis. Dicklyon (talk) 06:26, 23 June 2009 (UTC)

Solitons and nonlinear media

Some discussion would be advisable about the role of wavelength - velocity relation in a soliton, or more generally in water waves over a variable depth of water. Brews ohare (talk) 17:28, 22 June 2009 (UTC)

General response

Some interesting ideas there; many of these have been tried recently, but failed due to a lack of sources to connect the ideas to the topic of wavelength. Not everything about waves is relevant in the article on wavelength. If we only add topics that connected to wavelength in reliable sources, the article will be better for it. Dicklyon (talk) 06:26, 23 June 2009 (UTC)

de Broglie wavelength section

Brews, you have again come to insert your confusion about spectral decomposition and wavelength. I've reverted it, esp. since the sources you cite to support your interpretation don't use the word "wavelength" in connection with their spectral analysis. Note that the gaussian wave packet has a perfectly fixed wavelength, at least in the case where it's a sine wave times a gaussian envelope. This is not in conflict with it having a finite spectral width or a range of wavenumbers. I thought you said you were retired from trying to push your interpretation here. What happened to changee that? Doesn't appear to be new sources (at least not of the ones I checked). Dicklyon (talk) 19:01, 28 June 2009 (UTC)

I checked all your cited sources now. The few that use the word "wavelength" on the cited pages do NOT use it in a way that supports anything you said about it in that section. Please show me one if you disagree. Dicklyon (talk) 19:07, 28 June 2009 (UTC)

Dick: Your notion that the gaussian envelope times a sine wave of given wavelength has a perfectly fixed wavelength strikes me as nonsense because the Fourier transform of same is spread out over a distribution about the the wavelength of the sine wave, in accordance with the uncertainty principle if you like a physics explanation. Brews ohare (talk) 19:12, 28 June 2009 (UTC)

The definition of wavelength doesn't mention Fourier transforms. And uncertainty in wavelength is not the same as a wave having a range of wavelengths; even the uncertainty is better expressed in terms of wavenumber, since that's one of the variables that works in a Heisenberg-type relationship. Dicklyon (talk) 19:14, 28 June 2009 (UTC)

Wave packets and de Broglie wavelength

Dick: Maybe you can explain to me why the notion of superposing wavelengths to get localization is different from superposing wavevectors? It appears de Broglie thought they were simply reciprocals. Brews ohare (talk) 19:09, 28 June 2009 (UTC)

I don't think it would be production for me to try to explain it again. It's up to you to find a source that makes that connection. Dicklyon (talk) 19:14, 28 June 2009 (UTC)

Here you go: Barad Lyons Dahmen Brews ohare (talk) 19:24, 28 June 2009 (UTC)

I'll grant you the first one, odd though it is. The other two you're over-interpreting. Dicklyon (talk) 19:32, 28 June 2009 (UTC)

Dahmen:(b)Construction of a wave packet as a sum of harmonic waves of different wavelengths.

Lyons: Consideer a wave packet ....with each particular wavelength traveling a slightly different speed (as determined by the way the refractive index of the material depends upon wavelength)

Here's some more Manners David Bohm Boikness Schaum "such pulses can be obtained by superposing a large number of regular traveling waves of different wavelengths. Such a pulse is called a 'wave packet'

Need more?? Brews ohare (talk) 20:20, 28 June 2009 (UTC)

There remains an important distinction between what those sources say and your statements such as "To localize a particle, de Broglie proposed a superposition of different wavelengths ranging around a central value in a wave packet... In a wave packet, the wavelength of the particle is not precise, and the local wavelength deviates on either side of the center wavelength value." You had these citing sources that did not support them. If you put into the article only statements that are supported by the cited sources, I won't be able to object, will I? Dicklyon (talk) 20:26, 28 June 2009 (UTC)

So I'm going to have to present an extended discussion of wave packets so I can use only quoted material? Of course, I can't write an article on wave packet with sourced material and link it because that would be using Wiki to refer to itself as a source, yes? When k = 2π/λ, it's inadequate to cite a range of k is involved and 'therefore' a range of λ? Come on. Brews ohare (talk) 22:03, 28 June 2009 (UTC)

No, I'd suggest going the other way. You know how much I like your complicating extended discussions. Just stick to sources. Dicklyon (talk) 01:08, 29 June 2009 (UTC)

There's no doubt that a Fourier decomposition of a wave packet can be recast as an integral across different wavelengths. It's not very conventional, but some sources do that. However, you can't go from there to the statements you made in article. Dicklyon (talk) 01:23, 29 June 2009 (UTC)

New image

The new image needs to be modified to remove the dots along the curve. A sine wave is a smooth curve. It should not be presented with dots, unless the dots represent actual measured data. For this article, a smooth theoretical curve should be shown. I will remove the image from the article if it is not fixed soon.--Srleffler (talk) 23:39, 28 June 2009 (UTC)

Well, the trade-off here was make the curve clear by adding the dots (because my old version of Excel limits line widths) or have a thin line. Personally, I see no problem with the dots. They could be knots on a string or atoms in a lattice. The wave would still be a sine and the wavelength would be identified the same way. I think you are simply arguing aesthetics, not substance. Brews ohare (talk) 01:04, 29 June 2009 (UTC)

I'm arguing standard scientific graphing practice. Dots on a curve represent data, or represent a curve that is not continuous. The graph is not merely unaesthetic, it is incorrect.--Srleffler (talk) 03:38, 29 June 2009 (UTC)

I agree that the dots are obnoxious and distracting. Dicklyon (talk) 01:07, 29 June 2009 (UTC)

I removed the image for now, until it can be reworked. The old image is not aesthetic, but it is technically fine.--Srleffler (talk) 04:08, 29 June 2009 (UTC)

I updated the old image to show what was desired instead. An SVG would be good here if we were ambitious. Now that I have fig2svg in matlab, maybe I'll do that at some point. Dicklyon (talk) 04:50, 29 June 2009 (UTC)

I found how to fix the line width problem and re-did the figure which displays OK at thumb size. Brews ohare (talk) 18:44, 29 June 2009 (UTC)

Wavelength and mathematics of sinusoidal waves

It's probably a good idea to show how the wavelength appears in the expression for a propagating sinusoidal wave. The new section needs some editing for style, however. Wikipedia is not a textbook, and the style of this section seems more like a textbook than an encyclopedia article. It also seems to wander off-topic a bit, although it's probably good to introduce and link to wavevector and dispersion relation. I'll take a closer look at it tonight if I have time and nobody beats me to it.

A couple of quibbles:

• The text implies falsely that the exponential form is a plane wave and the sine form is not. Both are plane waves, to the extent that either represents a physical waveform.
• A physical wave is the real part of the complex exponential notation, not the imaginary part.

--Srleffler (talk) 17:02, 29 June 2009 (UTC)

Response to quibbles:

• • The article plane wave refers to a plane wave explicitly in the exponential form, as do the books I can find. I don't doubt that physically the sine form is also a plane wave, but I do not find that usage to be as common. The text emphatically does not say (or imply) a sine wave isn't a plane wave. I added a note to explain "plane wave" better. Brews ohare (talk) 21:50, 29 June 2009 (UTC)
  • A physical wave can be either the real or the imaginary part. Saying it is the real part gives you a cosine, and the imaginary part gives you a sine. They differ only in phase, so are equally "real". The earlier reference is to a sine (chosen because it avoids saying the cosine is is also a sinusoidal wave, with innumerable impeccable sources and several word-by-word quotations, eh?), so the imaginary part works better with the rest of the article. Brews ohare (talk) 21:10, 29 June 2009 (UTC)
    • AFAIK, it is conventional in EM theory to take the real part of the exponential form as physical. I don't recall seeing any source that does otherwise. I'm not sure the section on the exponential form is worth keeping anyway, though. What does it add to this article? It makes the text longer and harder to understand, but adds little value. Anyone who needs to know how wavelength is reflected in the exponential form will already know how to get there from the sinusoidal form.--Srleffler (talk) 22:34, 29 June 2009 (UTC)

Hi Srleffler: I agree that that convention shows up in EM; I don't know if it is completely general; I haven't chased down sources in elasticity, sound, and water waves to check it out. In any event, mathematically there is absolutely no preference for the Real over the Imaginary part. The way to fix this to suit you is for you to take the real part and then explain why the cosine shows up and how it relates to sinusoidal waves described by a sine function. Please be careful to include lots of solid citations that mention specifically the sine and the cosine in the same sentence with almost exactly the same wording that you use yourself. And make sure the word "wavelength" is included at least once. ;-) Brews ohare (talk) 00:23, 30 June 2009 (UTC)

The complex exponential form is, of course, the standard form in quantum mechanics for the wave function of a particle of fixed wavelength (equivalent to fixed momentum). In addition, all through the literature on waves, be it acoustic, EM, or QM, the exponential form shows up, so it seems useful to describe its connection to wavelength. It also is the common approach to link wavelength to wave vector. It is at least as useful as the real form to one trying to read the literature, and arguably far more useful in actual calculations than the sine wave form because of the many easy expansions of the exponential form that are well known. Stratton uses it all over the place, e.g.

And (shudder, shudder) it pops up in the Fourier transform. Brews ohare (talk) 00:18, 30 June 2009 (UTC)

I agree that the complex exponential form is by far the most common for people working in the field, and that anyone trying to read the literature in the fields you mention needs to be familiar with it. Anyone reading such literature, though, will not need this article to explain to them how wavelength is represented in the complex exponential form. They will already know it. I'm thinking that material is just too technical for this article. This article covers a pretty basic concept in physical science. If it isn't written at a level where an intelligent 11 year old can understand it, it's too technical.--Srleffler (talk) 01:52, 30 June 2009 (UTC)

Keep in mind that Wikipedia is not a textbook. It is neither necessary nor desirable to derive everything and bring in all possible mathematical detail in every article. This article needs to stay focused on wavelength, and needs to stay as comprehensible to a non-technical reader as possible. Details on the mathematics of wave propagation are best left to other articles.--Srleffler (talk) 22:34, 29 June 2009 (UTC)

So far the details on wave propagation have been brought up by Dicklyon. IMO nothing is derived here; it's a discussion of terminology and notation, with a few links to matters where wavelength shows up. Brews ohare (talk) 00:18, 30 June 2009 (UTC)

Whatever Dick may have brought in, you seem to repeatedly bring increased levels of mathematical detail into the article, often without regard for whether that material is suitable for the article.--Srleffler (talk) 01:52, 30 June 2009 (UTC)

Brews, please review Wikipedia:Make technical articles accessible. That summarizes what I have in mind regardling level of technical detail in articles.--Srleffler (talk) 02:43, 30 June 2009 (UTC)

Thanks for the link, which is helpful. However, I don't find it supports the notion that Wavelength should be written for 11-year olds. The basic call is whether "wavelength" has aspects beyond an eleven-year old level. It does, and they should be discussed, even if an eleven-year old is left out or forced to make an unusual effort. Brews ohare (talk) 03:11, 30 June 2009 (UTC)

Article Wavelength is for eleven-year olds

Quoting Srleffler just above to separate this topic:

"I'm thinking that material is just too technical for this article. This article covers a pretty basic concept in physical science. If it isn't written at a level where an intelligent 11 year old can understand it, it's too technical.--Srleffler (talk) 01:52, 30 June 2009 (UTC)"

Srleffler: It's clear that persons exist that wish to join the ranks of those for whom the complex exponential is a known quantity. Here's a place they might start. Where else in wikipedia is this information? Could it be linked?

And, what sets the level of "this" article? Are there specific criteria for this article, or is it in fact up to you and Dicklyon to set the bar? Why should the article all be written for 11 year-olds with no math or science? Couldn't some be for them, some for 16-year olds etc. etc.?

And last, it's a great strength of wiki to present things that bear upon the article, but are not necessarily directly on-topic. People regularly tell me they come here to get a lay-of-the-land and scope out the extent and connections of the topic. That requires some elbow room to introduce these adjacent matters in enough detail that the reader knows if it is of interest. Wouldn't even an 11-year old possibly find it fun to find wavelength leads to quantum mechanics and exponential wave functions? Brews ohare (talk) 02:53, 30 June 2009 (UTC)

Yes, there are people who may want to learn about complex exponential representation of waves. This isn't the right article for that. This article is about wavelength. I did not say that all articles should be written for 11 year-olds. I said that this article should be written at a level where an intelligent 11 year old could understand it. The reason this article needs to be simple, is as I stated above: it covers a basic concept in physical science. Wavelength is not a specialized subject, of interest only to an audience of professionals. It is not a subject that can only be treated with a highly technical exposition. It is a subject that can be explained well in plain English and simple mathematics. Per Wikipedia:Make technical articles accessible, it should be.--Srleffler (talk) 04:01, 30 June 2009 (UTC)

Srleffler, the only model I can come up with for Brews's behavior is that he is very pround of the symbol soup that he can cook up. He seems to have a very uneven understanding of basic concepts, yet is very deep into complex formalisms. He doesn't seem to understand that "plane" in "plane wave" is about the k-dot-r, the fact that the wave only depends on one dimension in three-space. He doesn't understand that it is conventional to use real part, or why. He doesn't understand how too much equation soup detracts from understanding, instead of adding to it. And he doesn't understand that after one says he's resigning from an article, he looks an ass to come back and start over again with similar and new attacks on it. Go figure. Dicklyon (talk) 04:11, 30 June 2009 (UTC)

Well, Dick is back in diplomatic form, making high school trig into complex formalism and attributing ignorance about k-dot-r that is off the wall. It is too bad that after a good night's sleep, Dick is so furious he can't say a simple useful thing, but just goes immediately into invective.

Srleffler says: "It is not a subject that can only be treated with a highly technical exposition. It is a subject that can be explained well in plain English and simple mathematics." Of course, like many technical subjects it has its plain English aspects and its technical aspects. Each should be treated in the appropriate fashion. Leaving out high-school math makes the article of little value as an introduction to the literature. Brews ohare (talk) 04:18, 30 June 2009 (UTC)

Actually I see Brews did define plane wave in a footnote, but it rather misses the point, since the direction is perpendiculat to the wavefront for any wave, plane or not, in an isotropic medium. The point of a plane wave is that the wave fronts are planes, so that direction is a unique constant direction. Dicklyon (talk) 04:40, 30 June 2009 (UTC)

The missed note says the wave fronts are planes of constant phase. It links wave fronts for further detail. Brews ohare (talk) 05:04, 30 June 2009 (UTC)

Brews, I see that you responded to my complaint about poor phrasing not by fixing the poor phrase, but by piling on more and more details about it: a footnote, a reference, a vague qualifier ("although only one of many ways to express a plane wave"), and a diagram of a plane wave. The text still introduces the complex notation by saying that it is "a form often referred to as a plane wave", implying that the other forms introduced in the article are not referred to as plane waves. All the extra doo-dads you added just confuse matters. Yes, the reader can probably now figure it out, but it's simpler to just not create the confusion in the first place. --Srleffler (talk) 05:32, 30 June 2009 (UTC)

Srleffler, I've done the work to convert Brews's long-winded version to a more concise version that doesn't lose anything important, I think. See if you agree. It could probably be simplified further. It might want some of his sources put back, though it's hard to disentangle those from the notes that he likes to put in footnotes. Dicklyon (talk) 06:41, 30 June 2009 (UTC)

Theory of colours

I don't like the link to Theory of Colours (book). I'll think a bit before deleting it, but it seems to me that from the standpoint of a modern understanding Goethe's ideas have much to do with how human colour vision works, something to do with dispersion in a prism, and little at all to do with wavelength. Newton's work on prisms is much more directly related to wavelength.--Srleffler (talk) 22:34, 29 June 2009 (UTC)

I put that in there because the other article that refer to the splitting of light with a prism are forlorn. Brews ohare (talk) 00:18, 30 June 2009 (UTC)

More Brews ohare idiosyncratic original research

Brews, all that stuff you added about adding up waves of different wavelengths to make wave packets is based on your idiosyncratic approach. I took out all the bits where the sources specifically did this in terms of wavenumber and didn't mention wavelength. To get a better handle on the usual approach, you can read the Fromhold ref, which explains that the wavenumber spectrum can be interpreted as a representation or our statisitcal knowledge of the wavelength. None of the sources support your idiosyncratic approach of describing spectral decomposition in terms of wavelength. And even if you do find a source that does it that way, it will be in a tiny minority. Let's just stick to what sources say about wavelength, and I won't have to keep getting so annoyed with you, OK? Dicklyon (talk) 16:42, 30 June 2009 (UTC)

I'd welcome a changed attitude. I am aware that I like a lot more detail than do you, but I can compromise. I hope you can keep the lid on while this happens. Brews ohare (talk) 16:50, 30 June 2009 (UTC)

The level of detail is not the issue. The level of irrelevant, idiosyncratic, unsourced, and improperly sourced distracting side junk is the issue, as we've explained repeatedly. Dicklyon (talk) 18:06, 30 June 2009 (UTC)

Beauty is in the eye of the beholder. I'd like you to support your decisions by more than statements of your preferences. Brews ohare (talk) 18:23, 30 June 2009 (UTC)

Have you ever found even one single beholder that supports your editing approach or your esthetics, here or at any other article where you're pushed idiosyncratic views and extreme expansions? Dicklyon (talk) 18:25, 30 June 2009 (UTC)

A most conciliatory attitude. I'd suggest one way to deal with me would be to (i) stop making cracks; (ii) support your positions not by blanket deletions, but by very specific suggestions for rewording or reorganizing; (iii) occasionally admit that I have contributed something. Brews ohare (talk) 18:58, 30 June 2009 (UTC)

Brews, your latest push, a 25% expansion to extend the article to quantum particles, using sources that still don't support what you say, is just showing that you are committed to your idiosyncratic approach, not to collaboration or consensus or to the quality of the wikipedia article. I'll try not to say what I think about this, but you can imagine. Dicklyon (talk) 18:17, 30 June 2009 (UTC)

What specifically is unsupported? Support is provided that de Broglie suggested wave packets. Support is provided showing superposition of sinusoids of different wave lengths can provide localization. Support is provided for the example of Gaussian wave packets. What are your detailed requests here? Brews ohare (talk) 18:21, 30 June 2009 (UTC)

As always, the detailed request it to only add material that sources connect to the concept of "wavelength", since that's the topic of this article. Dicklyon (talk) 18:23, 30 June 2009 (UTC)

There is a role here for wave packets because a wave of fixed wavelength is not a particle. Brews ohare (talk) 18:26, 30 June 2009 (UTC)

NB: this is an outdated model of quantum mechanics. While there is nothing wrong with using wavepackets to model the behaviour of quantum mechanical particles, there is nothing fundamental about this representation. A wave of fixed wavelength is as much a particle as anything else is. A monochromatic wave is a particle that never interacts with anything, and never decays. In modern quantum mechanics, one need not choose whether something is a wave or a particle. It is both, and neither.

Trying to introduce wavelength into quantum mechanics seems like an unnecessary complication. Frequency (or energy) and time are conjugate variables. Position and momentum are conjugate variables. Wavelength, as a spatial quantity, fits awkwardly. Note that wavenumber is a measure of frequency, and is explicitly not a spatial quantity in QM.--Srleffler (talk) 03:36, 1 July 2009 (UTC)

I did find a QM book that mentions wavelength as an alternative to wavenumber in analyzing wave packets, so I referenced it; but I rewrote this as a concise section on wave packets, with a main link to wave packet, since the connection of wave packets to wavelength is so marginal. Dicklyon (talk) 04:19, 1 July 2009 (UTC)

Another suggestion: the material you're adding would make more sense, and would find support in sources, in the wavenumber context. So why are you pushing it here, where it doesn't fit? Expand and correct wavenumber instead. Dicklyon (talk) 18:22, 30 June 2009 (UTC)

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