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  • need some information about resonance
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I think λ should be explained with a link to wavelength. Also I is not explained. The article should start with a definition, not with period and frequency.

The angular frequency formula is correct. --AxelBoldt

--- Reorganized concentrating on simpler topics first. Come on... don't formula look better in another font:

 like this?


Hmm. Sorry, didn't check this page before, I just changed it back. With my browser/settings, formulae look much better like this:

v = ω / k = λf ,

than like this:

  v = ω / k = λf .

But that's just for me. Feel free to change it back. -- DrBob

Examples of waves Sea-waves, which are perturbations that propagate through water (see also surfing and tsunami). Sound - a mechanical wave that propagates through air, liquid or solids, and is of a frequency detected by the auditory system. Similar are seismic waves in earthquakes, of which there are the S, P and L kinds. Light, radio waves, x-rays, etc. make up electromagnetic radiation. Propagating here is

'a disturbance of the electromagnetic field. '

does it want to mean that before "pass a light wave" there is a quiet magnetic field?

I agree that is was oddly formulated. I changed it. - Patrick 15:23 Feb 18, 2003 (UTC)

Perfect, but now i think there is another little incongruence. The first paragraph say about waves: "Waves have a medium through which they travel and can transfer energy from one place to another without any of the particles of the medium being displaced permanently". Is not correct to say that for all the kind of waves and to say a few lines later that electromanetic waves don't need a medium...

PS: I would correct it myself but my englis is very bad. (Sorry by the lot of mistakes that is sure I have wroten in this short comment).

I was not quite happy with this incongruence either; I have put the exception higher up. May be you can improve it further. Do not worry too much about the English, that can be corrected. - Patrick 22:54 Feb 18, 2003 (UTC)

It's confusing that "x" is used in the picture to refer to the amplitude. There is an equation down below where "y" is used. --dave

I've changed the image. If it is generally agreed that this new one is better, someone should go to the image discription page and delete the old one. Theresa knott 23:32 Apr 6, 2003 (UTC)

I am not happy with the sentence from the introduction where it says that particles oscilate around a fixed point. This is only true under "stationary" conditions, as every surfer knows. Which terminology can be used to describe phenomena like surf?

i am not happy with this recent addition, waves in ponds are circular: Waveguy 03:27, 28 Oct 2003 (UTC)

Ripples on the surface of a pond are actually a combination of transverse and longitudinal waves; therefore, the points on the surface follow elliptical paths.

I'm sorry. But I think that it is the 'wavefront' of the 'pond waves' (in case the initial disturbance is localized e.g. by throwing a stone in the pond)that is circular and not the nature of 'wave'. Any suggestions?Rahuljp

Your right Rahuljp. The ripple spread out in a circular pattern, but a point on the suface does not necessarily follow a sinusiodial path. Perhaps a diagram would make the matter clearer? (I'll get to work on one right away)Theresa knott 16:54, 6 Nov 2003 (UTC)

Thank you Theresa knott. But this does suggest that I did not use the correct language. Can you do it? Rahuljp

Personally I don't think I can do any better than you. IMO it's practically impossible to convey abstract scientific ideas with words. Pictures are much better. Theresa knott 17:13, 6 Nov 2003 (UTC)
Good job, Theresa. Rahuljp Thanks.I'm glad you liked it theresa knott 11:40, 14 Nov 2003 (UTC)
Pictures communicate concrete (actual, real) ideas (mental images). Words designate concepts that attempt to communicate abstract ideas.Lestrade (talk) 15:10, 2 February 2009 (UTC)Lestrade

I'm confused about ripples. Is it possible to provide an explanation of how a wave front moves? That is, consider the first wave front moving across a pond. At some moment a particle on the surface of the pond will be higher than it was previously. On the face of it, that is paradoxical. It is especially confusing since the water itself does not move with the wavefront--it's not like snow being pushed along by a snowplow. What is the explanation for how a bulge shape can move along the surface of the water? -- RussAbbott

Requestion peer review at wave vector. I just sort of made up this definition basd on what I've seen in papers and on some math website. I think it's okay, but see what you think. --Chinasaur 02:07, May 29, 2004 (UTC)


Several sections of this article need cleanup. The section Media is misleading (a general medium may by any combination or none of the classifications given). The secion on The wave equation also needs some rewriting, particuarly to avoid repeated use of "In the most general" and to explain the meaning of the various symbols used (x, y, z, and t)

done Ancheta Wis 08:36, 4 May 2005 (UTC)


This seems like a pretty obvious merger to me. Vanished user 1029384756 00:58, 25 July 2005 (UTC)

Merged articles Babbler 07:39, 5 August 2005 (UTC)


I am not sure if this is vandalism, but I removed:

"If you are in Merina Foster's Physics class this website will be no help whatsoever."

it was made by an IP adress, then changed by the same one Factoid 22:38, 4 January 2006 (UTC)

It might not be considered vandalism, but that sounds like a personal attack and should be deleted. --Austinsimcox 15:23, 22 February 2007 (UTC)

Standing Wave Math Expression[edit]

It seems being a paradox. For

\mathcal {\mid}\Psi(x,t){\mid}^2=A^2sin^{2}(kx)*cos^{2}({\omega}t)=0 {\neq}1

which means that it does not equal to 1. Thus caused not coresponse Normalization. Known a standing wave is expressed as

\mathcal, \Psi(x,t)=Asin(kx)*cos({\omega}t), .

Can anyone talk about your thoughts? Thanks.

By their math expression we can clearly find angular frequency of \mathcal V_p , \mathcal \omega which keeps constant when a wave vibrates up and down localized. That may because of energy transports into a wave is conservative,just like a particel moves up and down in a Y axis,localizedly(which keeps energy conservative).
But for another one,it travels in an X axis,that hints its phase-angular is the function of time. By time changes,then \mathcal \omega naturely changes either.

I'm a little not sure above. Could anyone discuss with me? --HydrogenSu 18:50, 30 January 2006 (UTC)


Regarding "For electromagnetic radiation, it is usually measured in nanometres." but what about e.g., 2-meter amateur radio etc.?!

Ripple diagram[edit]

I do not like the "elliptical trajectory" diagram. Trajectories are never elongated in the vertical, as drawn, but always in the horizontal, and only when the water is shallow. Also, the dashed red trajectory should not extend higher than the tops of the crests. This same diagram is part of the Ocean Surface Wave article, and I think it should also be changed there.Rracecarr 23:46, 10 May 2006 (UTC)

dreadfully deficient[edit]

For such a general article this seems to have neglected lots of things. For example I wanted to explore the general scope of resonance in waves in this article, but found nothing. John Riemann Soong 00:56, 28 July 2006 (UTC)


No, wave is a basic concept common in most of its meaning to advanced physics and everyday language, possibly unique in that regard. There may be special meanings that should be listed, but most uses of the word refer to the same concept and should lead to the same page, explaining that concept. David R. Ingham 07:05, 27 August 2006 (UTC)

Vote yes for disambiguation[edit]

Physics is not the only field with waves. For example, there is a wave theory in historical linguistics. And, there are waves in the invasion of a beachhead. Physical waves are not general enough to cover the social senses, so someone will have to take on more abstract definitions. There is also a quasi-physical sense, such as a wave of fire. And there are waves of feeling: dizziness, nausea, disappointment, hysteria, etc. Not to mention cultural waves. If we don't make the distinction today we'll be making it later on.Dave 03:29, 2 November 2006 (UTC)

Disagree. In my opinion, this is already a disambig page for the common wave concept used in the sciences. For example, it can be used for electromagnetic waves, seismic waves, etc. Besides, at the top, I see Wave (disambiguation) (immediately below the tag you inserted) for other uses of wave that doesn't involve the common terminology of reflection, wavelength, etc. +mwtoews 05:36, 2 November 2006 (UTC)
Right. I think the general wave concept is well explained here. I agree with Mwtoews. Lixy 16:33, 17 January 2007 (UTC)
Disagree I can see your point but I feel in almost all cases when somebody looks at the this page the information they are seeking is under the topics covered. I see a "wave of feeling" as an analogy of real waves. In other words, if you understand "wave" and "feeling" you'll understand "wave of feeling". There is a stronger case for attack waves in the military sense, but if such an entry is encyclopaedic it would seem to belong as a paragraph within an article on military tactics, not within "wave".
"Disagree" But any of those other waves are only called waves because they can be described rughly using the mathematical description of waves. That social descriptions use the concept of waves does not change the concept.

Move to B-class[edit]

I have moved the article to B-class because I think that it contains much of the content necessary to get to this grade —The preceding unsigned comment was added by Earth Network Editor (talkcontribs) 16:08, 13 February 2007 (UTC).

please help me please[edit]

does anyone know where can i type a question out then the webside will answer my questions

—The preceding unsigned comment was added by (talk) 14:40, 4 March 2007 (UTC).

Well, there isn't any magic "all questions answered here" portal, but you might have some luck at the Wikipedia Reference desk. -- MarcoTolo 22:42, 4 March 2007 (UTC)


I was looking for an article on Billows, you know, the things you push together to get a puff of air (often used to provide air to fires), but I got redirected here. I'm not really sure why. I'm also not sure why. I'm also not quite sure if that's the name of what I'm thinking of. Kevin 04:38, 23 July 2007 (UTC)

Try Bellows. -- MarcoTolo 04:59, 23 July 2007 (UTC)
FWIW, a billow can be "a large sea wave" according to this source. -- MarcoTolo 05:02, 23 July 2007 (UTC)
Ah. Kevin 04:13, 24 July 2007 (UTC)

Traveling wave[edit]

A travelling wave is not simple if the amplitude A is a function of z and t.Jalexbnbl 19:34, 11 September 2007 (UTC)


More about wave[edit]


This article does not interpret different waves, i.e. , plane wave, spherical wave, parapoloidal wave; in the article wave equation is concerning just the plane waves, not the other kinds, so it needs more revision.

A problem with the dipiction of the standing wave?

Please compare the standing wave on this article to a real standing wave at

There's an "illogicalness" to that standing wave. It gets longer when it's bended than when it's a straight line. A standing wave can not get longer as the wave propogates, it remains at a constant length -- doesn't it?

If I'm wrong about it please explain, but if I'm right please change that image immediately. --MrZhuKeeper (talk) 07:09, 13 December 2007 (UTC)

Spelling/grammar stuffs[edit]

I'm not sure what's trying to be said here, but it doesn't sound correct to me. Would somebody please change it?

From mathematical point of view most primitive (or fundamental) wave is harmonic (sinusoidal) wave which is described by the equation f(x,t) = Asin(ωt − kx)),

Is it "most waves are harmonic waves which are described"?


The two opposed waves each cancel the wave propagation of the other. This effect is known as waves.

Please effect changes with the effect of that making sense.

This comment left by thezeus18, who is too lazy to log on.


Unlike popular perception, any electromagnetic wave does not jump up and down. That is a portrait illusion. In reality, a wave looks like a coil and moves along a invisible tunnel-like path. When we say wavelength, we are really talking about the length of this coil.Anwar (talk) 19:05, 12 May 2008 (UTC)

May be so for some special cases, but this is a general article about wave phenomena in physics. So also sound waves, water waves, seismic waves, etc. Furthermore, electromagnetic waves are most often not generated by coils, e.g. in stars. So I reverted your edit. Perhaps you can also reconsider your addition of "coil" to other articles. Crowsnest (talk) 21:43, 12 May 2008 (UTC)

Basic wave equation[edit]

I'm having trouble understanding waves. I can see how rates of speed in circular motion can translate to expressed different kinds/shapes of waves and appreciate the descriptive graph/animations on the wikipedia pages for waves and trigonometry. But I don't believe it sufficiently explains why concepts of trigonometry like sin,cos which a beginner like myself associates with triangles are brought into describing waves, there is a connection gap. Elaborate on how sin, sohcahtoa, e.g. opposites divided by hypotenuse correspond and relate/interact to aspects of the waves .Dbjohn (talk) 10:56, 31 January 2009 (UTC)Dbjohn

Relation of waves and cycles?[edit]

Neither this article nor Cycle makes that clear. This article uses the words somewhat interchangeably. The latter article doesn't even bother to define cycle! Talking about this with my roommate who is much more scientifically inclined, I realize that these are very complex topics with a variety of applications, but not so complex that they should be ignored entirely in wikipedia. Thoughts? CarolMooreDC (talk) 15:32, 2 May 2009 (UTC)

Thanks for pointing this out. A wave is (often) an oscillatory – or cyclic – event that propagates through space. A cyclic event does not need to propagate. A solitary wave (water waves) is an example of a wave that is not cyclic, within the class of solitons. -- Crowsnest (talk) 16:19, 2 May 2009 (UTC)
Good start. Sounds like something that belongs in this article.
Turns out Cycle is a disambiguation page. Perhaps what is needed is an article Cycle (scientific). As discussed at Talk:Cycle#Problems_with_this_article. The question is would you be willing to help improve on that article per your obvious knowledge above? Thanks CarolMooreDC (talk) 16:52, 2 May 2009 (UTC)

Spatial and temporal relationships[edit]

Dicklyon has removed the contribution named as title to this section with the comment: remove disputed interpretation of wavelength of arbitrary periodic waves. The dispute appears to relate to the relation between wavelength of a wave described by

u(x,\ t) = F(x-vt) \ ,

and the periodicity of the function F in the case where F is in fact a periodic function of its argument. The math supporting the view that the wavelength and the period of F are one and the same appears to be very straightforward indeed, as expressed in the deleted material. This argument is as follows. Let the period of F be P, so:

u(x+P,\ t)=F(x+P-vt) = F(x-vt) = u(x,\ t) \,

which in words states that the wave u is completely unaltered by a translation through the period of the function F. That means, at a minimum, that P is some multiple of the wavelength of the wave. Actually, of course, the definiton of the wavelength λ of the wave is:

u(x+\lambda,\ t) = u(x,\ t) \,

and this relation cannot be satisfied for any λ < P. Therefore, λ = P.

A more mathematical argument is that any periodic function can be expressed as a Fourier series of sine waves, and the term of shortest wavelength has the same wavelength as the period of the function itself. Assuming no objection to the disputed statement when applied to a single sine wave, λ = P.

If there is some quarrel with this argument, I'd like to see it.

Assuming the math is accepted, the argument then must be that it is so convoluted as to require a source to back it up. If that is the issue, I would like to have it identified in so many words. Brews ohare (talk) 15:47, 6 July 2009 (UTC)

The math is fine. The dispute is about extending the applicability of the term "wavelength" to arbitrary periodic functions, rather than sticking with its traditional definition as the distance between crests or troughs. There's no need to move this dispute here while it's ongoing at wavelength. I only took out the minimal amount of stuff to avoid concluding that the spatial period is always called the wavelength. Dicklyon (talk) 15:56, 6 July 2009 (UTC)
Ideally, other editors will chime in and guide the decision about how to proceed here. Dicklyon (talk) 16:00, 6 July 2009 (UTC)

So, to be clear, do you think the material is incorrect (and if so how do you counter the math), or that the interpretation of the math is incorrect (and if so where is the identification of wavelength in error; the notion of crests and troughs is certainly included in the definition u(x+λ, t) = u(x, t)), or that a source is needed (and if so, to support what point exactly)? Brews ohare (talk) 16:01, 6 July 2009 (UTC)

The points of over-interpretation are just those points at which I excised the word "wavelength" from the text. Dicklyon (talk) 16:08, 6 July 2009 (UTC)
Since you put one back without so much as a comment here, I took it out again. Dicklyon (talk) 16:40, 6 July 2009 (UTC)
So, with the insertion of the word "spatial" are we now in agreement?? Brews ohare (talk) 16:43, 6 July 2009 (UTC)
Doesn't look like it, as you still have unsourced "mathematical definition of wavelength" that's more general than the usual definition. Also the article is suffering from your usual pattern of adding more verbiage and more equations instead of fixing or simplifying what's there. The next section as a whole seems like a perfect example of that syndrome. Dicklyon (talk) 17:11, 6 July 2009 (UTC)


Brews has a long-standing misunderstanding of the relevance of linearity in the applicability of sinusoid solutions to more general solutions. Just because a more general solution can be decomposed into sinusoids doesn't mean that sinusoidal solutions can be combined to make general solution; the latter requires linearity. Dicklyon (talk) 17:18, 6 July 2009 (UTC)

The characterization of my understanding as a "long-standing misunderstanding" is obnoxious and incorrect. The statement that Dicklyon makes that "Just because a more general solution can be decomposed into sinsusoids doesn't mean that sinusoidal solutions can be combined to make general solution; the latter requires linearity." is bogus. According to Fourier analysis, under extremely general restrictions upon a function f, f = Σan. Thus, for equally generous conditions, Σan = f. Dicklyon has not specified what strange or unusual cases he has in mind, but I'd guess the Fourier requirements meet all cases that need enter this article. Brews ohare (talk) 17:55, 6 July 2009 (UTC)
Moreover, linearity has nothing to do with use of Fourier series to represent a function. It is math. Perhaps Dicklyon is thinking about propagation in a physical medium: that is a separate issue of physics. For the discussion of the function f(x-vt), propagation of the rigid waveform is implied, whether or not there exists any real medium where that may happen. Brews ohare (talk) 17:55, 6 July 2009 (UTC)

The other dubious tag is on the so-called "mathematical definition of wavelength"; the citation that Brews added is to a property that follows from the usual definition of wavelength and the definition of periodicity. It does not claim to be making a more general definition of wavelength. Dicklyon (talk) 17:39, 6 July 2009 (UTC)

Wavelength of an irregular periodic waveform at a particular moment in time based upon a crest-to-crest separation or a trough-to-trough separation.
I am not claiming a more general definition of wavelength either. There are two ways to go on this topic. The first way is based upon the figure. If one adopts this view of wavelength, which is a direct adoption of the same definition used for the sine wave, then the definition u(x+λ, t) =u(x, t) is identical to the definition in the figure. Is there dispute over that point ?? Brews ohare (talk) 17:55, 6 July 2009 (UTC)
Alternatively, one may adopt the view that the concept of wavelength of the general waveform is not a defined concept, but that "spatial periodicity" must be used in this case, and the term "wavelength" reserved for purely sinusoidal forms. Is that Dicklyon's choice? Brews ohare (talk) 17:55, 6 July 2009 (UTC)

OK, I fixed it, reducing the section to a simple explanation without introducing new variables and bunches of unneeded equations. I kept a note to the effect that the spatial period is sometimes known as wavelength, since McPherson] uses it that way for arbitrary periodic functions (but he never says that's the definition, and never actually applies it to anything but a sine wave, so the "sometimes" allows also that this is not to be taken as a definition to be applied to draw conclusions that Brews wants to draw elsewhere). I think this is the best possible compromise. The bit about the Fourier analysis still doesn't make much sense, but it agrees with the source; decomposition into sinusoids makes a lot more sense in the context of dispersive media; for linear non-dispersive media, which allow solution by the d'Alembert formula, the result of using sinusoid decomposition is too trivial to matter, and in the nonlinear case that propagates something of that form it's inapplicable, since the sinusoidal components are not solutions of such a system. Dicklyon (talk) 05:13, 7 July 2009 (UTC)

Fourier series and wavelength[edit]

To begin, Pain says: "Any periodic function may be represented by the series:

 f(x) = \frac{1}{2} a_0 + a_1\ \cos x +a_2 \cos 2x + ... +a_n \cos nx + b_1 \sin x + ... +b_n \sin nx \ . "

In particular, at any given time t, any function f(x, t) that is periodic in x at that time t can be expressed as:

f(x, t) = \frac{1}{2} a_0(t) + a_1(t)\ \cos x +a_2(t) \cos 2x + ... +a_n(t) \cos nx + b_1(t) \sin x + ... +b_n(t) \sin nx \ .

If now xx + 2 π,

f(x + 2\pi, \  t) = f(x, \ t) \ .

Does one call 2π the wavelength of f ? Some authors do. For example, Rhodes says the first non-constant term has the same wavelength as the function f. Some authors do not. For example, Albarède calls it the period of f and says "this periodic length, called the wavelength λ in the case of harmonic waves, is the space analogue of the time period T."

I vote for using the term wavelength for all types of wave, and not just harmonic waves. Do you? Brews ohare (talk) 18:29, 6 July 2009 (UTC)

Indeed, that's the crux of many of our disagreements. In most fields, wavelength is the distance between crests. It's very unusual to see anyone refer to the spatial period of an arbitrary function as wavelength. It perverts the whole concept of wavelength, at least in fields that I'm familiar with (radio, radar, optics, sound, ocean waves, etc.). Dicklyon (talk) 19:45, 6 July 2009 (UTC)

The wavelength between successive crests or troughs (that is, successive overall maxima or minima) is what you see in the figure for wavelength of an irregular periodic waveform. That distance is the same as the spatial period of the wavefunction, and that definition agrees with the text in the article: u(x+λ, t) = u(x, t). Brews ohare (talk) 21:30, 6 July 2009 (UTC)

I don't see where Rhodes says what you say he does, but if he's does, it's not even mathematically plausible in general (if I interpret first non-constant term as meaning a term with nonzero ai with i > 0, then it's often not true if that first non-constant term has i > 1); point us at what he actually says. Dicklyon (talk) 20:04, 6 July 2009 (UTC)

On p. 24 Rhodes says about the Fourier series expansion of a periodic step, leaving out a few words here and there: "the second term f1 has the same wavelength as the step function, and wavelengths of subsequent terms are simple fractions of that wavelength." Please also look at the two citations in the article proper. Brews ohare (talk) 21:27, 6 July 2009 (UTC)

I can't see that page in google book search, but I found it in amazon; thanks for clarifying that what he said was not malformed like your paraphrase of it. Note that he's applying wavelength here to a repeating step function, or square wave, so there's no real need to generalize the usual definition to be consistent with what he says. I'm not sure what other citations you're referring to, but so far you've failed to show any source that supports your generalized definition. I'm sure a few must exist, so why can't you find even one? Dicklyon (talk) 22:18, 6 July 2009 (UTC)
If you meant the citations to Stein and Milton, I've already responded that neither of those has your generalized definition of wavelength, though they can be interpreted as consistent with it. They can also be interpreted as consistent with wavelength usually being applied to sinusoidal and nearly-sinusoidal waves. Dicklyon (talk) 22:27, 6 July 2009 (UTC)
Wavelength of an irregular periodic waveform at a particular moment in time based upon a crest-to-crest or trough-to trough definition.

Hi Dick: You're confusing me. You say because Rhodes treats a repeating step, no generalization is necessary. Is that because you see clearly what the wavelength of a repeating step is on the crest-to-crest basis? If so, probably you also see that works for a sawtooth wave, no? And by very slight extension to the wave in the figure. So, my question is, where does the crest-to-crest definition break down? In my view, it always applies. All we need is periodic behavior. Brews ohare (talk) 23:49, 6 July 2009 (UTC)

It breaks down for example in the notion of "global wavelength" that you were pushing on wavelength, where you wanted to define the wavelength of a periodic AM-modulated wave as its envelope repeat distance, rather than its crest-to-crest distance. Dicklyon (talk) 05:33, 7 July 2009 (UTC)

Following Rhodes, the Fourier series for any periodic function always begins (aside from the DC term) with a sinusoidal wave that has the period of the function approximated. (If it were a shorter wavelength term, the period of the function itself would be shorter too.) Consequently, following Rhodes, we can define the wavelength of any periodic wave form as that of the longest wavelength sinusoidal term contributing to its Fourier series. Brews ohare (talk) 23:45, 6 July 2009 (UTC)

That's just not true in general (it was true for the waveform for which Rhodes said it, but he didn't say it was general, because it's not); for example, if a1 is zero, but a2 and a3 are nonzero, the period is the period of the missing a1 component, but the period of the first non-constant or sinusoidal term is half of that. And even if you could define wavelength in some such way, can you point to anyone who does so? Not Rhodes. Dicklyon (talk) 05:33, 7 July 2009 (UTC)

As for references to support the definition u(x+λ, t) = u(x, t), the other one I had particularly in mind was Flowers. To roughly quote on p. 473: "A function f is periodic if f(x+ξ) = f(x). The constant ξ is called a period of the function. The smallest such period is called the fundamental period or simply the period of f, If x represents a space coordinate, then the period may instead be called the wavelength and is often written λ; if it represents the time coordinate, the period might instead be denoted by τ." I think that is very close to what I have said. Brews ohare (talk) 23:57, 6 July 2009 (UTC)

Close, but no cigar. McPherson, which I link in the section above, said something similar. Flowers says the spatial period "may instead be called the wavelength" and McPherson says "the distance it travels before it repeats is its wavelength". These are rather rare uses in the context of arbitrary wave shapes, and I now admit that they exist and you found them; but they're not really definitions, and don't look like they're really trying to claim to be. So, to make our article consistent with these, I've just put "sometimes known as wavelength", referenced McPherson, and let it go at that; no "mathematical definition", just an allowance that this usage is sometimes seen in sources, even though it's quite atypical (more typically, the wavelength of a sinusoid, by the usual definition of wavelength, is used to show these period time and space properties). Actually, now that I look at it, "the distance it travels before it repeats" is itself rather uninterpretable, isn't it? What is it that travels and repeats here? His "it" seems to be referring to "the maximum value that a wave can attain"; but then what of the it in "its wavelength"? What is that referring to? If the wave, the first it doesn't make sense. I hate to have to deal with such sloppy language in a source, but there it is. Dicklyon (talk) 05:33, 7 July 2009 (UTC)
As before, you have taken very precise and clear sources and claimed they are "rare", "not really definitions, "uninterpretable" and "sloppy language". None of these characterizations is valid, the sources are fine, they just don't agree with your prejudices. What can be clearer than Flowers: "A function f (x) is periodic if f(x+ξ) = f(x), for all x. The constant ξ is called a period of the function. The smallest such period is called the fundamental period or simply the period of f. If x represents a space coordinate, then the period may instead be called the wavelength and is often written λ " ? Brews ohare (talk) 15:00, 7 July 2009 (UTC)
That one is clear and precise, and I expressed no problem with it. The problem is with your interpretation that therefore every periodic function in space with a smallest period É… should be said to have a wavelength of É…. It doesn't really define É…, and doesn't claim that the usual practice of calling the wavelength of a wave its crest-to-crest spacing should be replaced by your notion of a "global wavelength" based on longer-term periodicity than the crest-to-crest wavelength. It's rare, it's not claiming to be a definition, and it says "may be called". I don't disagree with this source and what it says about periodicity, but I don't think it's attempting to define wavelength. If you can point out any field whether it is actually being used your way, we can reconsider. The McPherson source, however, is clearly sloppy and harder to interpret. Dicklyon (talk) 00:15, 8 July 2009 (UTC)
A bit confusing to me. The term "crest-to-crest" might be taken as the "local wavelength", which is not a unique number, but depends upon which adjacent crests are selected; or it may mean the separation of the largest crests. As Srleffler has pointed out to me, there is a statistical aspect to this, as the fine structure and the envelope are not deterministically related in some waveforms. Thus, the notion of "global wavelength" is better chosen as the "crest-to-crest" separation of the envelope of the signal. This is not an 'either-or" between the local and global wavelengths. They both have a role in describing the wave. Brews ohare (talk) 14:15, 8 July 2009 (UTC)
Here are some other approaches to wavelength. Begin in the time domain and define a periodic time behavior as one that satisfies f(t+T) = f(t). T is the period of the time behavior. Now consider a wave which has this time behavior at any chosen location in space. Then the wavelength of the wave is the distance it travels in a period T.(Source: Ramo, Whinnery and van Duzer.) How do you tell how far it travels? Sit on a point of given amplitude and measure how far it moves.
Which edition are you looking at, and what's the context? In 3rd edition the wording is slightly different, but it's clearly in the context of sinusoidal waves, not arbitrary periodic function. Elsewhere in the book (p.199) they say "we consider only sinusoidal excitation so that we can define a wavelength." Maybe if you'd start reading the sources, you'd understand how profoundly your POV deviates from theirs. Dicklyon (talk) 00:15, 8 July 2009 (UTC)
I've got the 1965 edition. The one-liner on wavelength appears in a discussion of plane waves on p. 326, and they do not discuss general waveforms at all. However, isn't it obvious from the general discussion of λ = vT that the definition of λ as how far the wave goes in time T is general? We have f(x-v(t+T)) = f(x-vt) -> vT = λ. Brews ohare (talk) 14:23, 8 July 2009 (UTC)
Here's another one: A wave is periodic in space, that is, f(x+P) = f(x). Make a Fourier series expansion. The wavelength λ is the longest wavelength sinusoid in its expansion.(cf. Rhodes) In fact, λ = P because any shorter λ in the series would mean f repeated itself with a shorter P.(Source: Folland.)
Rhodes did it for a particular waveform where the crest-to-crest distance is the wavelength, not for an arbitrary function where that definition would conflict. Dicklyon (talk) 00:15, 8 July 2009 (UTC)
There are two approaches additional to Flowers. They all agree, and are unambiguous. Any ambiguity about "sometimes known as wavelength" is not about what the wavelength is, but maybe about what you call it. Brews ohare (talk) 15:24, 7 July 2009 (UTC)
No, it's about what it is that is called wavelength. Dicklyon (talk) 00:15, 8 July 2009 (UTC)

Dick: Apparently we don't see these things the same way. You see conflict where I see unanimity. Let's start with this one:

"A wave is periodic in space, that is, f(x+P) = f(x). Make a Fourier series expansion. The wavelength λ is the longest wavelength sinusoid in its expansion.(cf. Rhodes) In fact, λ = P because any shorter λ in the series would mean f repeated itself with a shorter P."

First, do you agree that for a simple case like a sawtooth this approach results in the correct wavelength? If not, why not. If so, then why not for an arbitrary periodic waveshape? (For example, see Pain: "The fundamental, or first harmonic, has the frequency of the square wave." Rhodes "The second term ... has the same wavelength as the step function." This is no accident of square waves. See any tabulation of Fourier series for various waveforms. Of course, it can be proved mathematically for any wave shape using the formula for determining the coefficients of a Fourier expansion. See Eastwood "If B is a periodic function of the continuous variable x with a period length L then ... the wavenumber k takes only those values permitting integral numbers of wavelengths to fit in period length L.") Brews ohare (talk) 00:30, 8 July 2009 (UTC)

Sure, there's an uncountable infinity of cases where the period is equal to the period of the first non-constant Fourier series component; but you can't prove a claim by examples. I already disproved it by counter-example. Do you need an illustration? Dicklyon (talk) 15:41, 8 July 2009 (UTC)

An uncountable infinity is a lot of examples in support; please do provide your counter-example, which I do not recall. Perhaps you refer to this:

"If a1 is zero, but a2 and a3 are nonzero, the period is the period of the missing a1 component, but the period of the first non-constant or sinusoidal term is half of that."

For a1 to vanish, leaving only a2 and higher, the wave obviously has the periodicity of a2, and so the definition in terms of the longest wavelength term remains valid. Brews ohare (talk) 17:24, 8 July 2009 (UTC)

Example of signal where the lowest Fourier component's spatial period is neither close to the spatial period of the signal nor to its wavelength. The spatial period is four wavelengths, and the period of the lowest Fourier component is 4/3 the wavelength.
That is indeed the example; but what you say is obvious is quite wrong: it has the periodicity of a1, which is the least common period of the a2 and a3 sinusoids. An equivalent good example is an AM modulated signal with three components, corresponding to a carrier and upper and lower sidebands, with sinusoidal envelope. I made you a picture. Dicklyon (talk) 18:05, 8 July 2009 (UTC)
This would be a good time for you to acknowledge some of your errors, and fall back and study the sources and the math before continuing to insist on nonsense. Dicklyon (talk) 18:07, 8 July 2009 (UTC)

Hi Dick: You're right on this - this Fourier series definition of wavelength won't work in every case. However, this definition also is not actually used anywhere in the article, so it's moot, eh? Brews ohare (talk) 19:48, 8 July 2009 (UTC)

OK, sure, like arguments over most of your flaky assertions, they're moot if I make sure they're not in the article. It does serve, however, to prove how pointless it is to discuss mathematical logic with you. Dicklyon (talk) 01:16, 9 July 2009 (UTC)

Well, it's too bad we're back to invective. Brews ohare (talk) 03:42, 9 July 2009 (UTC) BTW, although a periodic function with period λ may in fact have no term in its series with period λ, all the terms in series have wavelengths that are fractions of λ, e.g λ; λ/2; λ/3; …; so it does remain possible to determine the λ of the function, but not always just by looking at the lead term. Brews ohare (talk) 19:25, 11 July 2009 (UTC)

Group velocity derivation[edit]

The derivation of group velocity in term of a wave packet, as sourced to Messiah's Quantum Mechanics, is considerably more complex than the typical classical derivation from the envelope of a pair of sine waves, which would agree with the illustration and would allow derivation without the integration over wavenumber space. Does anyone think we should re-do it the simple way? Dicklyon (talk) 18:25, 12 July 2009 (UTC)

Dicklyon, I think it should be redone in the more simple way. Simple is always best. Quinn (Ti-30X) 02:27, 13 July 2009 (UTC)
Simple may be best if simple is all you expect. However, I'd say the Messiah approach is simple as presented, involving only the knowledge of a derivative, which is unavoidable since group velocity is a derivative. It also provides an intro for the reader to a very commonly presented approach to this topic. If one wished to actually evaluate the integral using the method of stationary phase, that would be more complicated. However, that is not done, is not necessary. But for the interested, the link is there and the reference, which adds value to the approach.
Besides these arguments, the discussion is closely related to the other parts of the article on modulation and wave packets, and has some synergy there. I'd suggest that these connections may become more significant as the article evolves. Brews ohare (talk)

Why sine waves[edit]

In a string of edits (this net diff), Brews messed up the reason why sine waves are used in analyzing wave media. He demoted the introductory sentence that tried to say why we care about sine waves, namely that they are the unique shape that propagate unchanged in general linear time-invariant systems, so they can be characterized in terms of simply velocity or wavelength for each frequency. They are the eignefunctions. Brews not only demoted the reason, but also changed it to say "one shape that propagates unchanged" – but there are no others except in special cases. And he added irrelevant stuff like orthonormality (orthogonality is helpful, but not really necessary, and normality is completely irrelevant to the usefulness of sinusoidal decomposition). I'm tempted to revert the lot, but first thought I should seek comments and maybe Brews will fix his own. Probably we should move the paragraph to a subsection on "Why sinusoids" or something like that. Dicklyon (talk) 15:55, 14 July 2009 (UTC)

I believe Dicklyon is referring to media that are linear and dispersive.Leroy; Bansal. In non-dispersive media f(x-vt) propagates unchanged and can be characterized by wavelength and velocity, as shown by d'Alembert. Perhaps more has to be said, perhaps warranting a sub-section to explain the eigenfunction concept, as suggested. In view of the connection between dispersion and loss, it is not quite accurate to say the sine wave propagates unchanged: the sine wave is damped in time because of the loss. Brews ohare (talk) 17:30, 14 July 2009 (UTC)
But that's only true is non-dispersive media, which are a narrow special case; lossless or not, dispersion or not, sinusoids propagate with unchanging time-domain shape, which is why we break things into sinusoids. Without this property, they're not more special or useful than other bases you could use. If it were true in general that shapes propagate unchanged, there'd be little or no point in doing sinusoidal decompositions, since every arbitrary shape would be trivial to calculate the propagation of. The only other shapes of possible interest in this respect are the generalized sinusoids, including exponentially windowed and complex ones; but sinusoids are the unique real bounded shapes that have a relevant property to be useful in this problem. Dicklyon (talk) 18:06, 14 July 2009 (UTC)
Um, are you ignoring the fact that media with dispersion are lossy and sine waves are damped in lossy media, both in space and in time? Lai; Madelung Eq. 6.36; Tielens Eq. 5.16; Gale Eq. 2. At best, an approximation can be introduced that losses are neglected, curtailing the solution to a limited range of frequencies. Brews ohare (talk) 18:15, 14 July 2009 (UTC)

Incorrect image caption[edit]

The image which is captioned: "Wavelength of a cosine wave, λ, can be measured between any two points with the same phase, such as between crests, or troughs, or corresponding zero crossings as shown."

Actually demonstrates the wavelength being measured between two troughs, and it shows half the wavelength being measured by zero crossings. The wavelength being measured by peaks is not shown.

The caption seems very misdirecting. I'm not sure if the caption or the image should be updated. The image also demonstrates the semi-amplitude which the caption does not describe (but which a reader could easily confuse for the trough to trough wavelength measurement.) While this is explained in the main body of the text, perhaps the caption needs to be changed to reflect the fact the image demonstrates several features of the wave. —Preceding unsigned comment added by (talk) 01:38, 7 January 2010 (UTC) waves are caused bu wind —Preceding unsigned comment added by (talk) 00:13, 28 January 2010 (UTC)

About an image[edit]

about an image: a vertical line in the animation with the green and red dots to show one node of high freq, because its a bit of an illusion that the hf wave is not standing. —Preceding unsigned comment added by (talk) 04:51, 9 May 2010 (UTC)

Metachronal waves[edit]

I think reference to metachronal rhythm or metachronal wave belongs in the intro, but can't think how to word it. Meanwhile, I parked a reference under Other, --Pawyilee (talk) 14:07, 17 October 2010 (UTC)

Gravitational waves[edit]

I really can't see how gravitational waves are important enough, uncontroversial enough or explanatory enough to be right up at the top. Especially not with the qualyfier "Researchers believe..." If somebody feels the need for advanced physics in the introduction of the concept of waves, why not bring up the central concept of quantum mechanic wave functions instead of the peripheral and hypothetical gravitational wave idea? Niffe (talk) 11:36, 26 February 2011 (UTC)

Ok... since no one seems to disagree, I'll take the gravitational wave part out, or rather move it to its appropriate place. Niffe (talk) 12:01, 4 March 2011 (UTC)


Time is the reciprocal of distance, with one being defined in terms of the other. Treating time as an ephemeral dimension is the reciprocal of treating distance as the same. --Pawyilee (talk) 14:44, 27 February 2012 (UTC)

Non sinusoidal carriers[edit]

Are the equations in the section on Amplitude and modulation correct if the carrier is not sinusoidal? Must a carrier be sinusoidal? Thanks! --Lbeaumont (talk) 15:41, 21 February 2013 (UTC)

Can section be added to discuss energy transfer (and non-transfer) in waves?[edit]

Can section be added to discuss energy transfer (and non-transfer) in waves? Please see: for a more in-depth posing of this request. Thanks! --Lbeaumont (talk) 16:12, 21 February 2013 (UTC)


the gif with Dispersion has been removed. will be placed as a hyperlink in text. — Preceding unsigned comment added by Rlp17 (talkcontribs) 16:11, 19 May 2013 (UTC)

Air vs gas[edit]

Paul August reverted my edit to restore the language "air molecules" where I had changed it to "gas molecules." I am not intending to get into an edit war on this, but there is no such thing as an air molecule and it degrades WP's credibility to use such an inaccurate term, whether or not it is the custom. Altaphon (talk) 00:10, 19 November 2013 (UTC)

transverse vs longitudinal[edit]

Currently the only mention of transverse vs longitudinal is the last paragraph of the intro. Should we have sections on the features of these types? RJFJR (talk) 15:42, 22 May 2014 (UTC)