Stripes in Kundt's tube experiment

[Tazerfish]

To get this out of the way: I know how a kundt's tube generally works and how you can use it to determine the speed of sound.

For anyone who hasn't heard of it, you take a tube and "feed" it a resonant frequency.(very similar to a rubens tube)
The nodes of the resulting standing wave in the tube can be seen if you put dust in it.
The dust forms odd stripes I am concerned with in this thread.

(Alternatively you can put styrofoam balls in there)
The movement of the styrofoam balls is puzzling.
The dust particles probably move the same way when accreting into the stripes, they are just too small to see.

In the antinodes (of the air-displacement), the points where the air is moving back and forth the most, the styrofoam balls form "walls".

If you have never seen this before, here is a link
PRO TIP: Turn the volume down.

I thought about it for a while but I can't come up with a plausible explanation.
So I am asking you all,
why does it form the stripes/walls ?

 

[drvrm]

I thought about it for a while but I can't come up with a plausible explanation.
So I am asking you all,
why does it form the stripes/walls ?

At the particular frequency of vibration standing/stationary waves are created in the tube and the dust/cork powder get collected at the nodes where the displacement/velocity is minimum and measuring the distance between nodes the speed of sound in the medium can be measured.
see the details of experiment in any graduate level textbook or site like wikipedia/hyperphysics.

 

[Tazerfish]

At the particular frequency of vibration standing/stationary waves are created in the tube and the dust/cork powder get collected at the nodes where the displacement/velocity is minimum and measuring the distance between nodes the speed of sound in the medium can be measured.
see the details of experiment in any graduate level textbook or site like wikipedia/hyperphysics.

That does not explain the "walls" or stripes.
I am specifically talking about the buildup of thin vertical structures in the ANTI-nodes.
Not the general lumping in the node.

It may be of help to note that these structures are usually far smaller (about an order of magnitude) than the space you could call the antinode(about a quarter to half a wavelength where the stripes appear).I would have appretiated it if you gave this a more thorough look.
That is why I have posted THIS

To get this out of the way: I know how a kundt's tube generally works and how you can use it to determine the speed of sound.

I do not post a question here when I can easily find an answer on Wikipedia or a quick Google search.

PS:That wasn't supposed to be rude

 

[drvrm]

I do not post a question here when I can easily find an answer on Wikipedia or a quick Google search.

well, i am extremely sorry that i did not see the link before posting the previous comments/which necessarily escapes the focus of your question.
then i remember the experiment of stationary waves on a string ...Say Melde's Experiment or the resonance experiment on sonometer wire; it may be far fetched but the motion of string elements between the nodes are such that white loops are observed (due to persistence of vision)with a maximum displacement at the anti nodes ...in your experimental set up the material is forming those 'displacement profiles" however the type of material involved -its particle size is or becomes important.
In our labs the lumps of say "lycopodium powder' was there at the nodes but thin stripes of powder were found in between the nodes and we thought that due to various lengths of displacements along the stationary wave ,these deposits/spread perpendicular to the tube length is due to sudden stopping of the vibrations.( just like the loops of the white string).

 

[Tazerfish]

Don't be sorry.It was easy enough to miss.

This bit:

we thought that due to various lengths of displacements along the stationary wave ,these deposits/spread perpendicular to the tube length is due to sudden stopping of the vibrations

was a slighly confusing to read. I don't really understand how that would explain the stripes.
I think i get it now... Let me rephrase it : When suddenly turning the sound off, some of the material leaves the lumps at the nodes and deposits to form the stripes. Correct ?

While that is more plausible than some of the stuff I have come up with, I don't believe this is accurate.

Especially since I can assure you that the "stripe pattern" does form before the sound is turned off.(At least in our setup and in the styrofoam setup as well)
I would intuitively agree with you that the particle size is very important and we would have to look at these two problems, the styrofoam ball walls and the dust stripes, seperately.
Yet experiment seems to disagree.It at least looks like the clumping into stripes happens very similarly to the building up of the walls.

I have found this website http://tuhsphysics.ttsd.k12.or.us/Research/IB03/GeorInti/page/research.htm
examining the problem. I don't really agree with their hypothesis but they have collected some data that could be useful.
Take a look if you are interested.

It may be that friction with the bottom and between the particles is important...
At the anti-nodes you have high pressure gradients and the dust/balls get shaken rapidly with the air.
I could imagine a stripe pattern emerging from "jittering" a plate back and forth very quickly(without considering sound at all).
I have found a video talking about surface-tension-like properties arising from inelastic collisions in a somewhat related system:
I imagine in a tube, the easiest pattern to form would be stripes.

This idea obviously has its problems. For example, why would it not clump further and further (and then get pushed out to the nodes) until there was only very few concentrated areas, leaving the rest empty.

In my search I have also stumbled upon this:
http://www.physics.umd.edu/~reberg/services/demos/demosh3/h3-05.htm
(It has pictures that closely match our results)
As far as I have understood it, this reference indicates the actual resonances is similar to transverse modes in EM cavities and the link in the "suggestion" section seems to indicate the lumps (and maybe stripes) being caused by some kind of circulation.
It is fair to say that that went a little over my head.

 

[drvrm]

was a slighly confusing to read. I don't really understand how that would explain the stripes.
I think i get it now... Let me rephrase it : When suddenly turning the sound off, some of the material leaves the lumps at the nodes and deposits to form the stripes. Correct ?

In your second reference the picture of the stripes very much resembles our own experiment conducted in the graduate classes say in 1963...so i was sharing from memory.
i think one should look up the standing wave pattern on strings.. which we did in the same class both for longitudinal and transverse waves generated by electrically maintained tuning forks and will vary the tension on the string by putting weights and adjust the length to get standing waves.

The particles of the medium that is 'differential elements of the length of the strings" would produce a loop and the particles at the section of the loop will execute different oscillations(different amplitudes/maximum displacements) ;

so the anti nodes will have largest amplitudes...if we replace string...the connected elements by the molecules of the air(observed through Lycopodium powder(as they are very light and very small particle size)...they should exhibit the same pattern of motion ,that is from their mean position they should execute harmonic oscillations and there amplitudes will vary as we move from node to anti node;

no doubt it is due to two waves traveling in opposite direction.. but the resultant motion will be seen... this variation of the amplitude of the resultant motion is building the pattern...one can try to develop a theoretical model and in your reference the expt. with 'slinky' seems to be interesting. thanks for the references...
<We believe that since the sound waves are reflected off the closed end of the tube, the opposite waves colliding creates the raised columns. Since sound waves are longitudinal (that is, they are made up of alternating areas of high and low pressure), then when the waves collide, they create areas of intensely high and low pressure, pushing the styrofoam balls into columns in the shape of the wave.>
http://tuhsphysics.ttsd.k12.or.us/Research/IB03/GeorInti/page/research.htm

<For elementary classes, the motion of the dust can be compared with the motion of the coils in a SLINKY spring with longitudinal standing waves (G3-28: SUSPENDED SLINKY).>
http://www.physics.umd.edu/~reberg/services/demos/demosh3/h3-05.htm

i have quoted those two posts just to say that their attempts can be examined to unfold the mystery of the pattern. thanks again.

 

[Tazerfish]

I do understand what you were talking about with the string and how it applies to the motion of the dust.
However, I still do not have a specific and plausible explanation for why this motion would cause the "walls" to form.
What is making these patterns stable ?
Why does the top of the "wall" get pushed back into its equillibrium position when it tips?

<We believe that since the sound waves are reflected off the closed end of the tube, the opposite waves colliding creates the raised columns. Since sound waves are longitudinal (that is, they are made up of alternating areas of high and low pressure), then when the waves collide, they create areas of intensely high and low pressure, pushing the styrofoam balls into columns in the shape of the wave.>
http://tuhsphysics.ttsd.k12.or.us/Research/IB03/GeorInti/page/research.htm

This is the hypothesis I did not agree with.They basically explain the walls/stripes the same way the formation of the big lumps is explained.
But from my understanding of it, the pressure zones necessary for this behaviour wouldn't make sense.(they shouldn't be threre)
I am reasoably certain that their statement is incorrect.But I wouldn't dicard it just yet.

<For elementary classes, the motion of the dust can be compared with the motion of the coils in a SLINKY spring with longitudinal standing waves (G3-28: SUSPENDED SLINKY).>

While this does explain the motion of extremely light particles that are suspended in the air, it fails to explain the emergent phenomena like the stripes and walls.

The best hypothesis I have so far is this:

At the anti-nodes you have high pressure gradients and the dust/balls get shaken rapidly with the air.
I could imagine a stripe pattern emerging from "jittering" a plate back and forth very quickly(without considering sound at all).
I have found a video talking about surface-tension-like properties arising from inelastic collisions in a somewhat related system.
I imagine in a tube, the easiest pattern to form would be stripes.

That would not be a bad explanation.

You could test this hypothesis by trying out whether or not these stripe patterns would form under excitement by very loud non resonant sound(for example white noise). This "theory" would predict that the form of excitement does not matter much.
Another experiment to test the hypothesis would be to put in only very few balls and maybe take a long exposure photograph and then see whether the balls have been more in some areas of the tube than others.Of course you will see the overall node and antinode pattern but if the walls and stripes truly is a phenomena only arising as "group behavior" you shouldn't see the "wall" stripes.
In contrast, if there were pressure fileds that pushed the balls away from the space in between the walls, as the first reference implies you would see that even the single balls would be in some spaces more frequently and in others less frequently (basically like with the "walls").

But the behaviour of the styrofoam walls (similar to the stripes I mean) is not explained by my "lumping explanation" at all.
How come the walls are stable ?

I might have to add that the styrofoam balls could already be to heavy ( heavy as in mass / "drag" from the sound ) to really move "with the air".
If any of you have any new ideas ESPECIALLY concerning the stability of the walls let me know
And thanks for your engagement so far drvrm :)

 

[NascentOxygen]

Is this video showing a dozen or so separate groupings of powder over the span of a half-λ in the tube?

 

[Tazerfish]

Is this video showing a dozen or so separate groupings of powder over the span of a half-λ in the tube?

Yes, exactly.
Would you know more about that ?

EDIT:In my earlier posts, I forgot to mention that, the Wikipedia article attributes the motion of the particles to an effect called acoustic streaming, in which the absorption of sound (in the boundary layer) somehow produces a net flow.
But I don't know how these flows would look like in the kundt tube and whether they give a sufficient explanation for the stripes.

 

[NascentOxygen]

Could it be the harmonics? Even were the electrical signal a pure sinewave, the transducer probably has distortion. Do none of the videos on youtube address this?

Kundt's tube would be a good demonstration for the ISS.

 

[Tazerfish]

Could it be the harmonics? Even were the electrical signal a pure sinewave, the transducer probably has distortion. Do none of the videos on youtube address this?

Kundt's tube would be a good demonstration for the ISS.

Interesting idea(both the harmonics and the ISS experiment). I searched for some footage where they put a microphone, hooked up to an oscilloscope, into the tube and look out for the harmonics. Here is some footage .
There are some glitches and irregularities but I don't think it is enough.(with the closed tube you get "cleaner" signals)
Although it would be nice, I don't think it's the harmonics.

Five reasons. 1 If it was that simple I am reasonably sure people would know about it and it would be easy to find.
2.The spacing of the groupings is slightly irregular.
From my understanding that wouldn't happen if they were caused by the harmonics

3.The spacings don't vary much with the frequency(that is shown in one of the links I posted in post 5)
EDIT: The video I posted seems to indicate the opposite
4.The tones are usually very pure.The distortion shouldn't be enough.
5.I don't see any other mechanisms(besides the distortion) that would introduce the other frequencies.At least none with sufficient intensity

PS: I really like the idea of the experiment in space

 

[NascentOxygen]

Surely someone in a video must comment on the "striations"? Can people with a good ear for music listen to the video and judge whether the sound has overtones? It is very likely that the operator turned the sound volume up high for the purpose of making an impressive video, and running a small speaker at high volume equates to distortion. If you could find an example where volume is low, say, just enough to exhibit undulations at the fundamental, are those stripes still evident?

Your last video clip seems fixated on the striations, but my tablet/player won't display youtube comments. This one seems to be a high-speed study:

 

[Tazerfish]

OK. I think this is sort of solved now (not really, but the general process has likely been identified):
My teacher found an old book which talked about the "striations"(cool name btw).
The explanations using overtones seem to be a common misconception.

They supposedly form due to circulation induced by the high amplitude wave.
These flows circulate between the axis of the tube and the walls.
But the flows alone wouldn't produce these patterns.
When the air flows past the cork it forms eddies, which are said to carry the cork up and form the striations.

That sounds similar to the acoustic streaming mentioned in Wikipedia and the explanation here http://www.physics.umd.edu/~reberg/services/demos/demosh3/h3-05.htm[/PLAIN] especially the diagram under suggestions.

Sadly I do not have a good grasp on how exactly the standing waves induce these flows.(Apparently viscous dampening in the boundary layer is important)
And the details of the explanation are not clear to me.
Are the circulations almost steady or do they oscillate ?
How long are they ? half a wavelength? more? less?
How big are the eddies ? And what shape do the eddies and the general circulation have ?

A simulation (without the eddies at first) would really clarify it.Alternatively, observing the flow patterns in an experiment could be enlightening as well.
Now that I knew what to look for I just now found a paper on the topic of flows in the tube(filled with a liquid):
https://www.google.de/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&ved=0ahUKEwjgkcGn_5PPAhXMPRoKHa5aDsoQFggkMAE&url=https://smartech.gatech.edu/bitstream/handle/1853/20201/barfield_bobby_f_196508_phd_71124.pdf&usg=AFQjCNHIooY0JNMqeGIfUHffDnB-t1Lh2w&sig2=Mc33MRRtGPAQCHjnRfiyGA&cad=rja
That was really interesting
Page 21 to 22 and 41 to 44 gave the best insights into my questions.
The big circulations seem to be a steady, quarter wavelength long flow from node to antinode at the axis and back at the walls.
Apparently, under high enough energies, the circulation can stop beeing axis symetrical and form a big loop.The circulation then flows from node to antinode at the bottom and from antinode to node at the top.
At page 41 to 44 it is broadly outlined how the groupings are produced.

I have to say, it is fascinating how such a simple experiment can produce such complex and intricate phenomena.(The walls are only one of many mentioned in the article)

 

[arivero]

Note that the original document from kundts already show the striations

https://en.wikipedia.org/wiki/File:Kundt_tube.png

I find amazing how many youtube videos fail to mention the striations even when they are seeing them.

This other webpage https://sciencedemonstrations.fas.harvard.edu/presentations/resonant-fountain-tube proposes to consider also the standing wave in the glass cilinder... a sort of Chladni pattern, with the sound speed in the glass about ten times faster than the one in the air.

What I find uneasy of all these explanations is that they fail to predict the spacing of the stripes.

 

[arivero]

Ah, the original article of Andrade is free online at

http://rsta.royalsocietypublishing.org/content/230/681-693/413

This recent note confirms observations,
http://www.conforg.fr/cfadaga2004/master_cd/cd1/articles/000349.pdf

as well as some others in Amer J Phys etc.

 

[Mister T]

That does not explain the "walls" or stripes.
I am specifically talking about the buildup of thin vertical structures in the ANTI-nodes.
Not the general lumping in the node.

I can't get the video you posted to play. What you're describing is much smaller nodes and antinodes. These are due to higher frequency sounds, probably the higher harmonics.

 

[arivero]

No, it has been well stablished that they are not the harmonics, but probably this possibility explain why a lot of people does not pay atention nowadays. EDIT: you can see the image I linked from original papers of Kundt, figure 4, it seems that the issue of the "striations" were already discused and measured in the first experiments.

On my side I had expected it to be some interference pattern between the forced standing wave and the one from the generator, but it doesn't seem to be so, neither. They look so very much as the pattern in a double slit experiment that it is difficult to put it out of the head.

 

[sophiecentaur]

The explanations using overtones seem to be a common misconception.

That makes sense as the order of the overtone would be very high.
The use of the term 'striation' reminded me of the effect in a discharge tube. That is due to the mean free path of electrons through the plasma and they are constantly being accelerated and then ionising an atom, losing their KE and then accelerating again. It would be interesting to know how the spacing of the striations is affected by the size / mass of the powder particles. But is there a big range of dusts available? The actual depth of the powder doesn't seem to affect it in the videos.

 

[Mister T]

It's been awhile, but we used to use Kundt's tubes in a lab activity. We stroked a metal rod to create the sound source. Is it possible that those little ripples are due to the higher frequency longitudinal vibrations of the rod (as opposed to the lower frequency transverse vibrations of the rod). A similar thing can be heard from a guitar string when the guitar player's finger slides along a string and sets up higher frequency longitudinal vibrations in the string.

I don't think what I'm saying can be right, though, if people using Kundt's tube sources other than metal rods are also observing these same smaller ripples.

The smaller ripples you're seeing have ridges that run perpendicular to the long axis of the tube, right?

 

[sophiecentaur]

I can't get the video you posted to play. What you're describing is much smaller nodes and antinodes. These are due to higher frequency sounds, probably the higher harmonics.

If it were due to harmonics, the striations would change in periodicity drastically each time the fundamental frequency changed (phase change of fundamental times order of the harmonic) in fact they stay still as the fundamental changes by several tones of the musical scale.

 

[arivero]

The most fascinating thing is how similar the final shape is to the interference of two waves with a small difference of frequencies, but how the origin seems to be completely different.

 

[sophiecentaur]

Did anyone ever put a small probe microphone inside the tube and analyse the sound in there? That would eliminate any theory about harmonics or intermodulation products.
Alternatively, there could be a wave motion with a very low propagation speed and that could account for the short 'wavelength' of the striations. The sort of wave I'm suggesting would be a 'gravity wave' propagating over a 'pseudo' liquid, consisting of the particles being held in suspension by the shaking of the loudspeaker. The peak and trough shapes would match the sort of thing you get with a standing water wave in a shallow depth.