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It seems being a paradox. For

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

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

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

Can anyone talk about your thoughts? Thanks.

• One more question that what's difference between phase velocity and group velocity? My opinions and thoughts:

By their math expression we can clearly find angular frequency of ${\displaystyle {\mathcal {V}}_{p},}$ ${\displaystyle {\mathcal {\omega }}}$ 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 ${\displaystyle {\mathcal {\omega }}}$ naturely changes either.

I'm a little not sure above. Could anyone discuss with me?

--HydrogenSu 19:03, 1 February 2006 (UTC)[reply]

As someone familiar with Sound Theory, Im really disappointed with this article. There is hardly any reference to the effects of standing waves with regard to Acoustics & Sound waves. Ask any producer, sound engineer, audiophile, anyone who works with sound in spaces and theyll probably say standing waves are their biggest problems. It would be great if theres more info on how standing waves occur, how they disrupt the listening experience, methods to negate them and other subjects that relate to these waves acoustically. I would write something up myself, but i dont know enough about them to do so (hence,looking it up) !!! Shado.za 11:47, 2 June 2006 (UTC)[reply]

is there anybody else can say properly about this subject. i really need to know about standing wave..... — Preceding unsigned comment added by 161.139.212.162 (talk • contribs) 13:31, 13 September 2006 (UTC)[reply]

basically, if a string is set to oscillate (vibrate) from one end, and it is fixed at the other end, a wave travels along the string, until it gets to the end, where it is reflected back towards the other end. This is called superpositioning. By carefully adjusting the frequency of the string, you can form stationary waves, which is when the reflections occur so that a peak meets a trough, so they cancel (destructive interference). This forms a "node" point halfway along the string. Either side of the node point, a peak meets a peak, or a trough meets a trough, so they add together to create constructive interference. If the frequency of the open string is 25Hz, then there will be 2 standing waves when you double the frequency to 50Hz. 3 at 75Hz, etc etc. You can set a strobe light to flash at a similar frequency to "slow down" the motion of the waves. Hope this helps, Chris. — Preceding unsigned comment added by 88.110.66.44 (talk • contribs) 20:27, 19 September 2006 (UTC)[reply]

When two progressive waves having same amplitude , same period , same wave length and travelling in the same medium along the same line but in opposite direction superimpose, then the resultant of such two waves is known as Stationary wave or Standing wave.

This was added (with more typos in) to the main article. While having two similar definitions that don't really compliment each other can only create confusion, I don't really want to dismiss this explanation totally. I think this article is in need of a re-write, incorporating a lot more about the physical phenomena of standing waves and not just focusing on electrical engineering. I don't have time to do this myself but I think this and the explanation from the post above need to be worked into the article. OrangeDog 15:32, 6 November 2006 (UTC)[reply]

Dude im just a uni phisist but that definition is complete and utter bolloks. The resultant wave of two opposing waves doesnt have to be standing simply because they constructivly superpose.

Ok so maybe I didn't read it that closely but the article still needs work OrangeDog 11:28, 23 November 2006 (UTC)[reply]

On the subject of definition: I think you have mixed up two different types of wave: standing and stationary. A standing wave is, as your animation shows, oscillating in place. This would not be much good to a glider pilot. A stationary wave, on the other hand, has no time variation but does have a spatial wave structure. This is good for the glider pilot because he can sit in a fixed position where the air is rising. Would you object if I tried to split your article into two -- one on standing waves and one on stationary waves? mnjuckes 2 April, 2007

The definition says that there is a constant amplitude for all points along the axis of the wave, which seems like the definition of a stationary wave, not a standing wave.

eww @ you.

It sounds okay to me. The word "amplitude" means "maximum amplitude during a period". In a standing wave, the displacement varies sinusoidally with time, but at each point on the x-axis it has a unique amplitude (maximum value). --Chetvorno^TALK 12:24, 18 April 2015 (UTC)[reply]

you forgot the capitals. —The preceding unsigned comment was added by 202.59.80.55 (talk) 04:21, August 23, 2007 (UTC)

Do the two waves have to have the same frequency to add to a standing wave, or is this just a simple case? Smithg86 22:56, 17 October 2007 (UTC)[reply]

Does it mean moving the fluctuation up-and-down motion? Or a flow? Because rapids in a river is a flow, and that doesn't sound like a standing wave to me. —Preceding unsigned comment added by Bonzai273 (talk • contribs) 09:51, 20 April 2008

A hydraulic jump in water with a free surface is similar to a shock wave in air. It is called a standing wave since it does not seem to move, the jump propagation speed being equal (and of opposite direction) to the mean flow speed. Weak hydraulic jumps and near-critical flows (with Froude number near one) are also accompanied with an undular surface pattern, which is also a standing wave (the phase speed of the undulations is equal to the flow speed). Crowsnest (talk) 10:00, 21 April 2008 (UTC)[reply]

so is a "standing wave" as defined in a river caused by the hydraulic jump or by particular riverbed formations or obstructions? Usually the standing waves are in water at least a few feet deep, sometimes much deeper. They are also found mainly near rapids, I believe. In that case, is it still a transition between supercritical flow? I don't have a lot of knowledge on it but I've never seen supercritical flow deeper than a few inches. Then again, if I did, I probably wouldn't know it. Lime in the Coconut 19:35, 14 December 2009 (UTC)[reply]

Most commonly, I think, they're caused by boats suddenly decelerating, sending their bow wave down the river in front of them. OrangeDog (τ • ε) 20:09, 14 December 2009 (UTC)[reply]

Found an interesting link while searching for the answer. I think it must have to do with underwater obstacles (the waves are there, even with no boats). Here is the link: http://travel.nytimes.com/2009/07/10/travel/escapes/10Riversurf.html Lime in the Coconut 14:32, 15 December 2009 (UTC)[reply]

I removed the wave equation from the article, since:

1. it is far too complicated to start with a partial differential equation as the first mathematics in this article used by a general public,
2. it is one of many partial differential equations having standing wave solutions.

Crowsnest (talk) 05:36, 24 July 2009 (UTC)[reply]

Is this the appropriate place to add more practical information about the implications for sound? If not what's the right way to do that? —Preceding unsigned comment added by 68.160.181.190 (talk) 02:23, 14 August 2009 (UTC)[reply]

Depends what you mean by "practical". If you mean a how-to guide then that doesn't belong here, but if you have encyclopedic content to contribute, be bold and see what you can do. OrangeDog (τ • ε) 18:29, 15 January 2010 (UTC)[reply]

Moved from the article. OrangeDog (τ • ε) 18:27, 15 January 2010 (UTC)[reply]

DIFFERENCE BETWEEN STANDING NAD PROGRESSIVE MECHANICAL WAVES ON STRING: (1)IN STATIONARY WAVES ENERGY DOES NOT PROPOGATES IN SPACE BUT IT REMAINS CONFINED BETWEEN TWO ADJACENT NODES. (2)IN STATIOARY WAVES AMPLITUDE OF ALL PARICLES IS NOT NECESSARY SAME. (3)IN STATIONARY WAVE ALL PARTICLES COMES TO MEAN POSITION SIMULTANEOUSLY AND AS WELL AS ACQUIRES EXTREME POSITION SIMULTANEOUSLY. (5)IN STATIONARY WAVES ALL PARTICLES ACQUIRES MAXIMUM ACCELERATION SIMULTANEOUSLY OR MAXIMUM VELOCITY SIMULTANEOUSLY. (6)IN STATIONARY WAVES PORTION BETWEEN TWO ADJACENT NODES IS CALLED AS LOOP OR SEGMENT. (7)IN STATIONARY WAVES KINETIC ENERGY IS MAXIMUM WHEN ALL PARTICLES ARE AT MESN POSITION AND POTENTIAL ENERGY IS MAXIMUM AT EXTREME POSITION. (8)POTENTIAL ENERGY IS CONFINED NEAR NODE AND KINETIC ENERGY IS CONFINED NEAR ANTINODE. (9)IN STATIONARY WAVES IN A SEGMENT MECHANICAL ENERGY IS CONSERVED IN ABSENCE OF DAMPING BUT MECHANICAL ENERGY OF PARTICLE IS NOT CONSERVED,IT OSCILATES FROM NODE TO ANTINODE. (10)IN SATIONARY WAVE PHASE DIFFERENCE BETWEEN TWO PARTICLES IS EITHER ZERO OR PIE I.E. EITHER OUT OF PHSE OR IN THE PHASE.ALL PRTICLES IN SAME LOOP ARE IN PHASE.

In a travelling EM wave there is no phase shift between E and H. So can there be such a shift in a standing wave? The shift is illustrated by a picture in the article. —Preceding unsigned comment added by 83.28.180.109 (talk) 10:48, 2 April 2010 (UTC)[reply]

This is because the reflection happens on the surface of an conductor, oh which the E field is 0, whereas the H field gets reflected with a phase shift. You can explain this via the Maxwell equations. Hope you understand I'm not native english =) Nabrufa (talk) 13:14, 11 May 2010 (UTC)[reply]

i created a new standing wave related image, i present it here incase anyone wants to stick it in the article anywhere

how about combining and harmonic as they are sort of related. and not all pages reference to all three as related.

--someone —Preceding unsigned comment added by 121.222.120.22 (talk • contribs) 04:49, 9 May 2010

@Chetvorno:

...a standing wave – also known as a stationary wave – is a wave which at each point in its medium has a constant amplitude.

A travelling wave generated by a constant source will also have constant (peak) amplitude at all points in a medium. In particular, a plane wave travelling down a lossless transmission line will have constant amplitude down the line. More accurately, the essential properties of a standing wave are; no net transfer of energy and infinite SWR. A finite SWR implies a wave that can be decomposed into travelling wave and stationary wave components (assuming a linear medium). SpinningSpark 18:51, 13 October 2017 (UTC)[reply]

I agree, the existing definition is wrong; thanks for catching that. The SWR definition you give looks correct and I think it should be added to the article, but it's not going to mean much to most general readers; anyone who knows what SWR means knows what a "standing wave" is. It's kind of circular; SWR itself is defined in terms of the max and min of the standing wave. Can we find a definition for the intro that just uses concepts like amplitude, phase and position? --Chetvorno^TALK 20:16, 13 October 2017 (UTC)[reply]

I agree that SWR is not the essence of the definition. The essential thing is that the peaks of the wave do not move spatially. Infinite SWR and no transfer of energy are consequential effects which can be described in the body of the article. I have sources to hand so I'll write something along those lines tomorrow. It's too late to do it tonight. SpinningSpark 23:29, 14 October 2017 (UTC)[reply]

Can someone fix the formatting for the gallary in the "Opposing waves" section?

It appears that the movie file of "Kayakers surfing a standing wave in Great Falls National Park." located above the gallery in the previous section is pushing the gallery to the left.

It is only "fixed" if I zoom in to >150% on a 1080 monitor.

I don't quite know how to fix it, but if someone does could they kindly reply to me here about how to fix such things in the future?

--Davidjessop (talk) 16:22, 22 March 2021 (UTC)[reply]

O.K I fixed it using the previous fix from CharbelAD which was to add an empty line.

I still think this fix could be improved to work with any resolution

--Davidjessop (talk) 16:27, 22 March 2021 (UTC)[reply]

Hello. The best way to "fix" the size of thumbs is to go to click your Preference link in the upper right corner and then click the Appearance tab. You can set the size of thumbs to your preference. Constant314 (talk) 21:24, 22 March 2021 (UTC)[reply]

In the section on "Opposing waves", an image showing the first 6 harmonics was captioned: "Standing waves in a string – the fundamental mode and the first 5 overtones." This same image is used further down in the section "Standing wave on a string with two fixed ends" "Standing waves in a string – the fundamental mode and the first 5 harmonics."

The second instance was added later, and has a factually incorrect description. As per the page on Harmonics: "A harmonic is a wave with a frequency that is a positive integer multiple of the frequency of the original wave, known as the fundamental frequency. The original wave is also called the 1st harmonic" "Harmonics may also be called "overtones", "partials" or "upper partials". The difference between "harmonic" and "overtone" is that the term "harmonic" includes all of the notes in a series, including the fundamental frequency (e.g., the open string of a guitar). The term "overtone" only includes the pitches above the fundamental." "n = 2 2nd partial 1st overtone 2nd harmonic"

This indicates the first instance description is correct, with it being the fundamental frequency and the first 5 overtones; which could also be labelled as the first 6 harmonics, or the fundamental mode and the next 5 harmonics. The image description for the second instance incorrectly implies that the fundamental is not a harmonic and incorrectly implies that the 1st harmonic is not the fundamental frequency. I propose updating the second instance to match the first, with both having the simple description: "Standing waves in a string – the fundamental mode and the first 5 overtones." But when I made this change it was reverted.

While I am fine with other options for the wording, I do not want it to be what it is now as that is facually incorrect and contradicts other pages. Does anyone have any objection to that wording, and if so, can they state what they think it should be and why? Black.jeff (talk) 00:00, 21 September 2021 (UTC)[reply]

Hello. Perhaps I didn't look carefully. Harmonics are integrally related to the fundamental whereas overtones don't have to be. Harmonics are overtones, but in the figure the looked like harmonics, that is they appeared to be an integer multiples of the fundamental. The literature mostly uses the term harmonics. Constant314 (talk) 00:23, 21 September 2021 (UTC)[reply]

I agree with that, and in that way harmonics may be best. The issue comes when that interger is 1, where the 1st harmonic is the fundamental frequency. Would you prefer the text "Standing waves in a string – the fundamental mode and the next 5 harmonics." and for that to be on both images?Black.jeff (talk) 00:41, 21 September 2021 (UTC)[reply]

I see what yo mean. I changed the other occurrence. Constant314 (talk) 02:08, 21 September 2021 (UTC)[reply]

I think you may have misunderstood. The image shows the first 6 harmonics. This is the fundamental frequency which is the first harmonic, as well as the next 5 harmonics. The current wording indicates that the fundamental frequency is not a harmonic; while my understanding is that the nth harmonic has a frequency of n times the fundamental frequency, making the first harmonic the fundamental frequency. Overtone avoids that confusion and is likely why it was used initially. I also note that the section on standing wave on a string with 1 fixed end also incorrectly describes what I think should be the third harmonic as the first (with only odd numbered harmonics being possible in this case). Do you agree with that, or is your understanding that the first harmonic is not the fundamental frequency? Black.jeff (talk) 06:12, 21 September 2021 (UTC)[reply]

As anyone who has read through the talk section of this Wikipedia page would know, the precise definition of what a standing wave is has been a subject of discussion here several times. Standing waves have always been problematic in physics education, because they are closely related to waves but, strictly speaking, standing "waves" aren't waves as they don't propagate. Attempting to fix this contradiction by classifying waves as being stationary waves or progressive waves is logically inconsistent with the definition of what a wave is, therefore making it bad (although unfortunately common) practice. Instead, if you really think about it, standing "waves" are really oscillations formed by the superposition of other waves (note that this is noticeable in a GIF of standing wave formation, such as the one presented in this article). Many people here would already be aware of this idea (it's even hinted to in the standing waves definition presented in this page) and technically speaking, it's more correct. Though, unfortunately, this more precise oscillatory description is not universally used because the inaccurate, misleading wave-like description has, over ages of scientific education, become the traditional, go-to definition for standing waves. I therefore acknowledge that it is unlikely that this better description will be installed as the primary definition of what a standing wave is, so all I will propose is that it could be a good idea to mention something along the lines of this alternative, (semi- and/or quasi-) equivalent definition of standing waves:

Standing waves are oscillations formed by the superposition of periodic waves (such that the quotient of their frequencies/periods is rational) propagating in opposite directions.

Many would be quick to raise questions about my definition, and that's absolutely valid. One obvious, major point of concern regarding this definition is how it doesn't assert identical frequency/period, wavelength, equilibrium value, (peak) amplitude nor coherence but, as a matter of fact, periodic waves that superimpose as they propagate in opposite directions do not necessarily need to fulfil such conditions to form standing wave oscillations (and, in fact, they do not even need to be perfectly periodic [e.g. like the over-idealistic abstraction of a wave with an impeccable sinusoidal waveform that is perfectly maintained throughout propagation], it should still work as long as they have frequencies that divide to a rational number). If one would like to visualise this for themselves, they may use the slider animations on the graphing website desmos.com by introducing two waveforms (say of the form y₁ = A₁ sin(ω₁x + θ₁ + t) + C₁ and y₂ = A₂ sin(ω₂x + θ₂ - t) + C₂ such that ω₁ / ω₂ ∈ ℚ), by use of the variable x for the waveform itself and the slider variable t to make them move (like a wave would), and adding/superimposing them (i.e. y_{superposition} = y₁ + y₂) to then observe how any point in the resultant superposition pattern will oscillate back and forth at a constant rate (like a standing wave would).

Anyways, aside from that, I'm certain that my vague alternative definition could do some refinement and polishing, after all I still have a number of doubts about all this stuff myself. Please correct me if I am incorrect about anything or if there's any important details I have missed, I've just always been bugged by standing "waves" and wanted to somehow help fix up this dilemma (not saying that important, well established stuff such as stationary & progressive waves should just be entirely abolished and removed from this page). This is not intended to be a harsh criticism, just a suggestion for potential improvement. Xyqorophibian (talk) 03:40, 29 September 2025 (UTC)[reply]

• Standing waves are oscillations formed by the superposition of periodic waves

This is not an improvement as standing waves can be nonlinear.

Kind regards, Roffaduft (talk) 09:01, 1 October 2025 (UTC)[reply]

Ah right, nonlinearity.

That complicates defining these things quite a lot, but hopefully another alternative definition (that is compatible with nonlinearity) for standing waves will be brought up.

Thank you for the correction, @Roffaduft.

Best regards, Xyqorophibian (talk) 09:48, 1 October 2025 (UTC)[reply]

The root claim in the original post is "standing "waves" aren't waves as they don't propagate". This assertion makes no sense to me. Physics distinguishes standing from traveling wave even among linear waves. Johnjbarton (talk) 04:23, 7 October 2025 (UTC)[reply]

Hello @Johnjbarton, I've mentioned my reasoning before in here.

A wave is defined as "a propagating dynamic disturbance (change from equilibrium) of one or more quantities" (i.e. the definition of waves on the Wikipedia article on waves), the inclusion of "propagating" in this definition implies that a wave can't be spatially fixed.

Since standing waves don't exhibit net propagation (like actual waves do) but instead they alternate in place (like oscillations do), they wouldn't really qualify as waves.

And, as I've also previously stated, this typical practice in physics of distinguishing actual ("progressive/travelling") waves from standing "waves" (i.e. oscillations, not waves as such) is just contradictory (towards the previously stated definition) and conflative (between waves and oscillations) even when taking into account linearity and nonlinearity.

Please correct me if I happen to be mistaken.

Best regards, Xyqorophibian (talk) 06:40, 7 October 2025 (UTC)[reply]

The wave definition on wave is bogus, so conclusions based on that definition are not useful. See Talk:Wave. Johnjbarton (talk) 15:54, 7 October 2025 (UTC)[reply]

Well then at this point it's just a matter of what one defines a wave as being in the first place.

Gonna read more about the new topic you started in Talk:Wave.

Kind regards, Xyqorophibian (talk) 20:47, 7 October 2025 (UTC)[reply]

I couldn't find anything written about de Broglie standing waves nor gravitational standing waves here, I think they may be worth mentioning.

On the Wikipedia page for matter waves, it is mentioned that the superposition of de Broglie Waves to form standing waves is of significance to molecular chemistry. Since this is in relation to the concept of standing waves, it'd make sense to mention standing matter waves here.

Though gravitational waves have only recently been experimentally discovered and little is known about them, the theoretical possibility of gravitational standing waves is quite niche (largely due to the tremendous mathematical complexity, scarcity of knowledge in relation to and the extreme unlikeliness of such a phenomenon) but has definitely been explored and it may be a potentially good idea to include in this standing waves article as well as the article for gravitational waves.

There are also various other kinds of standing waves (whether observed, theoretical or semi-theoretical) that could be elaborated more on in this article, and I agree with the author of this talk page's "Acoustic Standing Waves?" topic on how more could be written about standing sound waves. I'm eager to hear other people's thoughts (whether on this topic or my previous one) and possibly learn something new. Xyqorophibian (talk) 04:21, 29 September 2025 (UTC)[reply]

Update:

I think I'd like to retract my suggestion regarding gravitational standing waves, after discussing the topic on the talk page of the Wikipedia article for standing waves, I have been informed that the topic doesn't really meet the notability guidelines for Wikipedia. And even aside from that, the citation was improper (sorry for that, should've been

Szybka, S. J., & Cieślik, A. (2019). Standing waves in general relativity. Physical Review D, 100(6), 064025.).

Though perhaps de Broglie standing waves could still be mentioned? Xyqorophibian (talk) 00:34, 30 September 2025 (UTC)[reply]