Can this relationship be derived between Schrodinger equation and Doppler shift?

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Offline timey

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Can this relationship be derived between Schrödinger equation and Doppler shift equation?

Looking at Chladni plates and the resulting node patterns versus a laser beam trained on a mirror super glued to a speaker cone, causing the dot of the laser beam to form a pattern when a tone/frequency is applied - could there be a relationship between node patterns and lissajous curves?

Let's say we have a Chladni plate of a reflective/mirrored surface, and having established node patterns at varying frequencies, would lissajous curves (?)  be established at the same frequencies by pointing a laser at the surface?

And considering that the node pattern is caused at the points of least vibration of that frequency, and that the laser is depicting movement caused by the extremities of the vibration of that frequency - could it be said that the patterns created are the inverse of each other?
« Last Edit: 04/10/2016 13:16:38 by chris »
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Offline evan_au

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could there be a relationship between [Chladni] node patterns and lissajous curves?
Chladni patterns are caused by the resonance of a physical object when subjected to a drive at a single frequency. This highlights the areas of high and low amplitude vibrations in the plate.

Lissajous figures are created when you drive a light by two different frequencies in the X and Y axes, where those frequencies are harmonically related to each other.

They can both produce interesting patterns, but they are different patterns.

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Can this relationship be derived between Schrödinger equation and Doppler shift equation?
The Chladni patterns are derived from physical resonances of a macroscopic object with varying shape, thickness and (in the case of wooden instruments) the wood grain, glue, bracing struts, lacquer and sound holes. By varying the frequency of the incoming sound, you could graph the spectral response of resonances to the incoming sound.

Doppler shift of a laser beam can be used to measure the frequency of vibration of the object from which it is reflected. By graphing this in two dimensions, you could reconstruct the Chladni pattern.

Schrödinger's equation describes the electron energy levels of an atom. By exciting the atom with difference frequencies of light, you could graph the spectral response of resonances to the incoming light.

You may try (with great difficulty) to construct an instrument that has similar resonances to the Hydrogen spectrum. If the Hydrogen spectrum had energy levels related to 1/n, this may even be compatible with the Pythagorean ideal of harmony.

However, the actual energy levels of Hydrogen are related as 1/n2, so the harmony could be described at best as "complex", but most people would just call it "noise".
See: https://en.wikipedia.org/wiki/Rydberg_formula#Rydberg_formula_for_hydrogen
« Last Edit: 07/10/2016 21:39:39 by evan_au »

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Offline timey

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Doppler shift of a laser beam can be used to measure the frequency of vibration of the object from which it is reflected. By graphing this in two dimensions, you could reconstruct the Chladni pattern.

It is this part of what you say that is of most interest to me, but first:

With regards to the Chladni plate node patterns...

You say that Lissijous curves or figures are caused by the harmonics created by driving 2 frequencies, but that the node patterns on the plate are caused by driving only 1 frequency...  Lets examine this a bit.

https://m.youtube.com/watch?v=lRFysSAxWxI

Here we see that there are 4 differently structured plates being used.  If you hang each plate as a gong and hit it with a gong striker, each plate will have its own naturally occurring frequency.  As far as I can tell, please correct me if wrong, what the bow is doing is adding another frequency to the plate that resonates with the plates natural frequency.  As the video shows, by bowing at different placements of the rim of the plate, the bow can add one of a few different frequencies which resonate/harmonise with the plates natural frequency.  But there are only so many frequencies that will harmonise with the plates own natural frequency.  Note how the placement of thumbnail on an exterior line of the node pattern, and the placement of the bow on, or between node lines changes the pitch in steps.

https://m.youtube.com/watch?v=wvJAgrUBF4w

Here we can see that this plate structure can only cause node patterns when subject to certain frequencies.  The frequencies that can achieve node patterns on this structure are surely mathematically linked to the structures own natural frequency?  Are all the frequencies that create node patterns on this structure following scale to the structures own frequency?

If so then the Chladni pattern is also created by driving 2 frequencies to harmonise/resonate, surely?

https://m.youtube.com/watch?v=RxzMzSZF_b4

Correct me if I'm wrong but these laser patterns must be caused by Doppler shift right?

https://m.youtube.com/watch?v=t6nGiBzGLD8

To get further understanding I watched the above.  Please note the use of the timing function.*

Correct me if I am wrong, but isn't the node pattern's association with Schrödinger due to standing wave function in that a wavelength can only fit x amount of times within a confine?

https://en.m.wikipedia.org/wiki/Wave_function_collapse

Quote:
"Significantly, the combined wave function of the system and environment continue to obey theSchrödinger equation.[4]"
Unquote:

* http://physics.stackexchange.com/questions/29551/quantum-explanation-of-doppler-effect

The second answer in relation to the first is interesting in relation to SR comments and time perturbations.

As you pointed out, node patterns are created in the areas of least vibration in the plate.
The Lissijous patterns are being created by the extremities of the vibration of the mirror.
I realise, as you have pointed out, that the patterns are not the same patterns, but given that each produced a pattern associated with the same frequencies, it interested me if one would be the inverse of the other?

So... If the Lissijous pattern is being caused by the Doppler shift of the laser beam, how would one mathematically graph this in two dimensions to reconstruct the Chladni pattern?
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Offline Colin2B

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As far as I can tell, please correct me if wrong, what the bow is doing is adding another frequency to the plate that resonates with the plates natural frequency.  As the video shows, by bowing at different placements of the rim of the plate, the bow can add one of a few different frequencies which resonate/harmonise with the plates natural frequency. 
The bow doesn't add a frequency, it adds vibrational energy that allows the plate to resonate at one of its natural frequencies. Each frequency creates a different pattern caused by the standing waves. Lower order modes - those with fewer node lines - require less energy to initiate them, the simplest and lowest order being the cross/star pattern, which occurs at the lowest frequency. By bowing with differing amounts of force, ie energy, the bower can cause higher order modes to appear, you will also note that he uses his thumb nail to force a node at certain locations which produces a different mode and can bow at different points to encourage different antinodes.
What isn't clear from these videos is that the patterns are more complex than they appear at first sight. Although we see only antinodes, one antinodes might be going up while another goes down. Sometimes adjacent corners will move in opposite directions as the plate twists.
« Last Edit: 05/10/2016 00:04:24 by Colin2B »
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Offline timey

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OK - I'm following your logic, and agree that there is evidence in the video that suggests that some of the complexity of how the patterns change from one to another is lost...

But Colin, isn't stating the bowing adding an energy to the situation in as much as saying the bow is adding a frequency?  Energy has a frequency, right?  Bowing with added energy, or at a placement on the edge of the plate that causes higher or lower energy, or by placing a thumbnail at a node point to alter the distribution of the added energy, these energies are all accompanied by their associated frequencies.  Note that some of the bowing ie: added energy/frequency does not cause node patterning.  The bowing has to be just so, or a tone/node pattern cannot be achieved.

In the second video it is shown that frequencies are being driven to the plate directly.  This can also be considered to be a case of adding vibrational energy, but the machine kindly translates this added energy into its associated frequency for us.  Note that the node patterns are only formed fully at specific frequencies, albeit some of the complexity as the patterns change seems to be lost.

My thoughts drifting towards thinking (subject to being wrong of course) that these specific frequencies that the patterns are fully formed at are harmonics to the plates own frequency.  A frequency that is related to the plates own energy of e=mc^2.

So in light of what I've mentioned, do you think a Chladni plate pattern is involving 2 frequencies, like the Lassijous figures do, or is it just 1 frequency?
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Offline evan_au

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Quote from: timey
do you think a Chladni plate pattern is involving 2 frequencies, like the Lassijous figures do, or is it just 1 frequency?
I was thinking of exciting the vibrations with a sine-wave generator, which is just 1 frequency.

If you were adding energy with a violin bow, I guess you could imagine a rectangular plate with sides in a 3:1 ratio.
If you bowed near a corner, I guess you could set up vibrations which are harmonically related in different axes, and use that to produce Lissajous figures.

Even when you are bowing a violin string, it is normal to produce several harmonics in the same string, simultaneously.

If you activated the Chladni pattern with a loudspeaker, you could feed in two different tones to excite two different resonances at the same time.

Quote
isn't stating the bowing adding an energy to the situation in as much as saying the bow is adding a frequency?
Colin is the luthier here, but my simple understanding is that the keratin flakes of the horse-hair have a sawtooth edge, which repeatedly pulls and releases the string (or plate, in this case). This represents a fairly broadband stimulation of any resonances.

These frequent small knocks can build up into a large oscillation at the natural resonant frequency of the object.
- I assume the location, pressure, speed and direction of the bowing can accentuate or inhibit particular vibration frequencies.
- Or it can produce a chaotic screech, like most beginner violin players...

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Offline Colin2B

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My thoughts drifting towards thinking (subject to being wrong of course) that these specific frequencies that the patterns are fully formed at are harmonics to the plates own frequency.  A frequency that is related to the plates own energy of e=mc^2.
….
So in light of what I've mentioned, do you think a Chladni plate pattern is involving 2 frequencies, like the Lassijous figures do, or is it just 1 frequency?
You're in the right direction but veering off to left field.
I may have assumed understanding of what vibrational modes involve, so perhaps we need to step back a bit.
Let's take the standard vibrating string in every school textbook. Fixed at both ends if we pluck the middle we get that characteristic shape of antinode in the middle and nodes at each end. You might be excused for thinking that the centre of the string is just moving up and down, but it's more complex than that. As Evan says, all vibrations of this type involve more than one frequency, in this case when plucked at the centre the string will vibrate in all modes where there is an antinode at the centre and nodes at each end and if you draw them out you will find they are the odd harmonics of the string fundamental. In theory you should have all the odd frequencies, but as fourier analysis shows the components of a square wave are the odd harmonics up to infinity and the mechanics of the string mean that it can't support all the harmonics. If you superpose the harmonics up to about 9 you will get an envelope very similar to the one in the textbooks showing the average excursion of the points along the string – average excursion because the harmonics get out of phase so the string ends up doing some interesting contortions rather than the implied moving up and down at the centre.
Plucking at different points eg ¼ along the string, will excite a different series of harmonics.

When you look at analysing the Chladni plates you can view them as 2 dimensional open ended pipes – antinodes at the outer edge. As with strings, vibrating pipes and plates all generate multiple frequencies, but it is the mix of frequencies that give the specific patterns on the plates.

isn't stating the bowing adding an energy to the situation in as much as saying the bow is adding a frequency? 
As you can see from the string example, plucking doesn't add a frequency if just allows the string to vibrate in its natural manner.
Let's look at a simple plate, a school ruler. If you hold one end on the desk and twang the end the ruler will vibrate at its natural frequency. If you bow the end of the ruler (ie plate) the rosin on the bow grips the end of the ruler and pushes it down, when the return force of the spring in the ruler overcomes the grip of the bow the ruler springs back and again will vibrate at its natural frequency.
The bow isn't adding a frequency, you could just as easily twang the edge of the Chladni plate or tap it with a stick, all would cause it to vibrate in a particular mode depending on where you hit it. However, you would have to twang it a lot of times before the sand moved to the nodes, the bow or a loudspeaker is easier.

E=mc2? No. There is mass of the plate, which affects the frequency of the modes. There is a speed which is the wave speed of sound across the plate, that is largely determined by E, Young's Modulus. But we aren't dealing here with mass energy equivalence, much more basic.

Schrodinger? Well, the mathematical tools used in acoustic analysis eg fourier analysis, eigenvalues etc are all part of QM, but the Shrodinger  equation is a very specific wave analysis not part of the analysis of string and plate vibrations.

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Offline timey

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Colin - although your description of harmonics is highly relevant, it is something that will be obvious to anyone who has played a string instrument (Yup, I was a screechy violinist as a child Evan...(chuckle)) ...or inspected the inner workings of a piano, which I do and have.
(although I must say, in that I have worked with music, that I was literally horrified when watching the oscilloscope video at the extent of that which I didn't know and probably still don't know...)
No instrument makes a sound of itself.  An instrument always requires an input of vibration to resonate with.  All vibrations have an associated frequency, and all a frequency is, is the amount of vibrations per standard second.

Schrodinger? Well, the mathematical tools used in acoustic analysis eg fourier analysis, eigenvalues etc are all part of QM, but the Shrodinger  equation is a very specific wave analysis not part of the analysis of string and plate vibrations.

What you are saying here is not really correct.  Please see link:

https://en.m.wikipedia.org/wiki/Ernst_Chladni

Quote:
" In quantum mechanics, Chladni figures ("nodal patterns") are known to be related to the solutions of theSchrödinger equation for one-electron atoms, and the mathematics describing them was used by Erwin Schrödinger to arrive at the understanding of electron orbitals.[12]"
Unquote:

If this venture into advanced mathematics is being off left side then off left side is exactly where I want to be...

A Chlani plate node pattern relates to the Schrödinger equation - and the Lissijous figures, by the nature of the mechanics that are involved in their creation, must relate to the Doppler shift equation.

A node pattern is caused at the areas of least vibration.
A Lissijous figure is caused by the areas of most vibration.
The question being: Could node patterns be the opposite, or inverse, of Lissijous figures?

I am looking for the mathematical relationship between these patterns and am thinking that "phase shift' might be relevant?
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Offline jeffreyH

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Colin - although your description of harmonics is highly relevant, it is something that will be obvious to anyone who has played a string instrument (Yup, I was a screechy violinist as a child Evan...(chuckle)) ...or inspected the inner workings of a piano, which I do and have.
(although I must say, in that I have worked with music, that I was literally horrified when watching the oscilloscope video at the extent of that which I didn't know and probably still don't know...)
No instrument makes a sound of itself.  An instrument always requires an input of vibration to resonate with.  All vibrations have an associated frequency, and all a frequency is, is the amount of vibrations per standard second.

Schrodinger? Well, the mathematical tools used in acoustic analysis eg fourier analysis, eigenvalues etc are all part of QM, but the Shrodinger  equation is a very specific wave analysis not part of the analysis of string and plate vibrations.

What you are saying here is not really correct.  Please see link:

https://en.m.wikipedia.org/wiki/Ernst_Chladni

Quote:
" In quantum mechanics, Chladni figures ("nodal patterns") are known to be related to the solutions of theSchrödinger equation for one-electron atoms, and the mathematics describing them was used by Erwin Schrödinger to arrive at the understanding of electron orbitals.[12]"
Unquote:

If this venture into advanced mathematics is being off left side then off left side is exactly where I want to be...

A Chlani plate node pattern relates to the Schrödinger equation - and the Lissijous figures, by the nature of the mechanics that are involved in their creation, must relate to the Doppler shift equation.

A node pattern is caused at the areas of least vibration.
A Lissijous figure is caused by the areas of most vibration.
The question being: Could node patterns be the opposite, or inverse, of Lissijous figures?

I am looking for the mathematical relationship between these patterns and am thinking that "phase shift' might be relevant?

Well done.
Fixation on the Einstein papers is a good definition of OCD.

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Offline alancalverd

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A Chlani plate node pattern relates to the Schrödinger equation - and the Lissijous figures, by the nature of the mechanics that are involved in their creation, must relate to the Doppler shift equation.

A node pattern is caused at the areas of least vibration.
A Lissijous figure is caused by the areas of most vibration.
The question being: Could node patterns be the opposite, or inverse, of Lissijous figures?

Lots of muddled thinking here.

Chladni figures are the inverse distribution of amplitude over a resonating body, and can in some cases resemble atomic orbitals. 

Lissajous figures are the patterns produced by the intersection of two sinusoidal curves the axes of which are at right angles to each other. Where the frequencies are in a harmonic relationship such that the phases of the two curves are locked, the figure appears static. Nothing to to with resonance or orbitals, just the 2D solution of two simultaneous equations. And although not truly Lissajous, you can use a similar XY plot on an oscilloscope to investigate the phase relationship of any two periodic signals.

The Doppler shift equation is a scalar only. df/f = v/c where df is the change in observed frequency, v is the relative velocity of source and observer, and c is the velocity of sound/light/whatever. No sinusoids or spatial coordinates.   
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Offline Colin2B

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What you are saying here is not really correct.  Please see link:

https://en.m.wikipedia.org/wiki/Ernst_Chladni

Quote:
" In quantum mechanics, Chladni figures ("nodal patterns") are known to be related to the solutions of theSchrödinger equation for one-electron atoms, and the mathematics describing them was used by Erwin Schrödinger to arrive at the understanding of electron orbitals.[12]"
Unquote:

Yes, I know the history which I why I made the comment about the commonality of the maths tools.  However, as I said the Shrodinger equation has a very specific application and you can't turn it round and use it to analyse Chladni patterns or reach conclusions about Doppler shift on the laser beam. As Evan pointed out:
Schrödinger's equation describes the electron energy levels of an atom. By exciting the atom with difference frequencies of light, you could graph the spectral response of resonances to the incoming light.
You may try (with great difficulty) to construct an instrument that has similar resonances to the Hydrogen spectrum. If the Hydrogen spectrum had energy levels related to 1/n, this may even be compatible with the Pythagorean ideal of harmony.
However, the actual energy levels of Hydrogen are related as 1/n2, so the harmony could be described at best as "complex", but most people would just call it "noise".

Returning to your original question:
..considering that the node pattern is caused at the points of least vibration of that frequency, and that the laser is depicting movement caused by the extremities of the vibration of that frequency - could it be said that the patterns created are the inverse of each other?
Pointing a single laser at the mirror surface won't create an inverse of the pattern as you need a way of mapping the areas of maximum displacement (as the inverse of the map of nodes), however you could use laser holography to do it.

PS We'll have to agree to disagree on whether the bow is inputting a frequency or just activating the natural resonance modes of the plate.



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Offline timey

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A Chlani plate node pattern relates to the Schrödinger equation - and the Lissijous figures, by the nature of the mechanics that are involved in their creation, must relate to the Doppler shift equation.

A node pattern is caused at the areas of least vibration.
A Lissijous figure is caused by the areas of most vibration.
The question being: Could node patterns be the opposite, or inverse, of Lissijous figures?

Lots of muddled thinking here.

Chladni figures are the inverse distribution of amplitude over a resonating body, and can in some cases resemble atomic orbitals. 

Lissajous figures are the patterns produced by the intersection of two sinusoidal curves the axes of which are at right angles to each other. Where the frequencies are in a harmonic relationship such that the phases of the two curves are locked, the figure appears static. Nothing to to with resonance or orbitals, just the 2D solution of two simultaneous equations. And although not truly Lissajous, you can use a similar XY plot on an oscilloscope to investigate the phase relationship of any two periodic signals.

The Doppler shift equation is a scalar only. df/f = v/c where df is the change in observed frequency, v is the relative velocity of source and observer, and c is the velocity of sound/light/whatever. No sinusoids or spatial coordinates.   

Sorry, no muddled thinking here on my part.  You just have not bothered to read the thread and therefore are unaware of the context.

Please read post 2 and observe the videos that have already outlined what you have posted, and the link to physics stack exchange and answer 2 in relation to answer 1, which will give you the context.  I am thinking that phase shift is the common ground.

There are some outstanding issues that are a bit muddling though and perhaps you can indeed help.
The first being:
-is a Chladni plate being driven to resonance by 2 frequencies? ie:  its own inherent frequency/tone resonating with the frequency associated with the input energy... to create harmonics of the plates natural frequency as the input  frequency is increased.  Or is there just 1 frequency involved in a Chladni pattern, as Colin says?
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Offline alancalverd

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Back to the "frequency" of a chladni plate. It doesn't have an inherent  single frequency. All that is required of a vibrating plate is that there is a node(s) at the point(s) of suspension. You can then, in principle, set up any number of standing waves whose nodes correspond, by bashing it hard enough. Continuous input to a symmetrcal plate by a violin bow will select for those harmonics with antinodes at the point of contact. If you are very good at bowing, you can select just the fundamental of a circular plate, which will give you a circular pattern with a single frequency only. 
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Offline timey

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When the plate is not being vibrating, (ie: does not have an input) the structure already contains standing waves...doesn't it?
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Offline Colin2B

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When the plate is not being vibrating, (ie: does not have an input) the structure already contains standing waves...doesn't it?
No, there is no standing wave until the plate is vibrating at the specific resonant frequency for that standing wave(s).
« Last Edit: 06/10/2016 18:53:41 by Colin2B »
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Offline timey

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So the plate does not have an energy associated with its mass, and De Broglie matter waves are only mathematical conveniences with which to calculate quantum probabilities?

Or do you mean that there is no visible evidence of standing waves in the structure until an input frequency resonates with one or more of the inherent standing waves harmonics...

Otherwise what in the plate is the input resonating with please?
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Offline Colin2B

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So the plate does not have an energy associated with its mass, and De Broglie matter waves are only mathematical conveniences with which to calculate quantum probabilities?
I don't see the relevance of this. We don't need to use quantum level calculations to calculate vibrations in large scale structures. Of course the plate has an energy associated with its mass, but we are not looking to convert any of that mass to energy or vise versa, neither are we interested in its relativistic kinetic energy.

Or do you mean that there is no visible evidence of standing waves in the structure until an input frequency resonates with one or more of the inherent standing waves harmonics...
No, I mean that there are no standing waves until the plate vibrates. Standing waves are vibrations, they are the characteristic patterns of the resonances.
The input frequency does not resonate with anything, it is the plate which resonates at certain frequencies. The input frequency doesn't change its form.

Otherwise what in the plate is the input resonating with please?
I think there is a confusion of terminology here and understanding of resonance so it might help to step backwards and forget about input frequencies for a moment.

Imagine you ping the edge of the plate with a plectrum. The plectrum pushes down the edge and releases it, the speed at which the edge returns towards its undeformed position will determine the frequency at which the plate 'rings', this speed is in turn determined by the stiffness of the plate (its springyness) and its mass (inertia) and the dimensions of the plate. This is an oversimplification, but it is intended to illustrate that there is nothing inside the plate which resonates, but it is the plate itself - governed by its physical characteristics - which resonates. Also, it does not need an input frequency in order to resonate just some action to set it going.
The use of a loudspeaker as an initiator is useful because it provides a continuous stimulus and also allows us to see at which frequencies the resonances occur.
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Offline timey

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I understand your take in the sense of analysing sound Colin, but what I'm interested in is the relationship between the Chladni patterns and the Schrödinger equations, the related analysis of wave function at quantum level, the relationship that the Lorentz transformations have in relation to Doppler shift at quantum level, the time perturbations that are used to calculate at quantum level...
And the relationship that Lissajous figures have with the electron.

Any energy added at this level is significant to frequency and therefore is relevant to standing wave function.  The properties of the plate are significant because they are quite simply properties that are inherent to the plate and these properties affect the effects of any input energy. (Energy mass equivalence asside for time being)

Here we can see that Lissajous figures can also be traced out by sand dripping from a compound pendulum.

https://www.britannica.com/topic/Lissajous-figure

http://www.differencebetween.com/difference-between-simple-pendulum-and-vs-compound-pendulum/

Quote:
" What is the difference between Simple and Compound Pendulums?
• The period and, therefore, the frequency of the simple pendulum depends only on the length of the string and the gravitational acceleration. The period and the frequency of the compound pendulum depend on the length of gyration, the moment of inertia, and the mass of the pendulum, as well as the gravitational acceleration.
• The physical pendulum is the real life scenario of the simple pendulum."
Unquote:

An apparatus of frequency vibrated mirrors causing a laser beam to trace out Lissajous figures is physically equal to the actions of a compound pendulum...
Lets say the mirror was engineered to be resonant at a pure tone (the same tone as was used to create the Lissajous figure) and sand were placed on the mirror being vibrated (at same other tone that created the Lissajous figure) ...then a Chladni pattern would emerge...?
And if so, what would the mathematical relationship be?
« Last Edit: 07/10/2016 10:01:21 by timey »
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Offline Colin2B

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...it is the relationship between the Chladni patterns and the Schrödinger equations, the related analysis of wave function at quantum level, the relationship that the Lorentz transformations have in relation to Doppler shift at quantum level, the time perturbations that are used to calculate at quantum level...
And the relationship that Lissajous figures have with the electron.
Ok, I may have misunderstood what you are trying to do here. It sound like you are trying to draw some conclusions about actions at the atomic level using chladni, lissajou and Doppler, rather than trying to use shrodinger, e=mc2, etc to analyse the plates.

Here we can see that Lissajous figures can also be traced out by sand dripping from a compound pendulum.
This type of compound pendulum is in fact 2 simple pendulums linked, one oscillates as a sine wave in x direction the other in y so that their combined motion is the lissajou curve. Sorry to labour this but it is important to recognise that the curves are the result of combining 2 pure sinewaves.

An apparatus of frequency vibrated mirrors causing a laser beam to trace out Lissajous figures is physically equal to the actions of a compound pendulum...
Yes, you could cause the mirror to vibrate on 2 axes perpendicular to each other across the face of the mirror, each axis would need to vibrate with a sinewave.

Lets say the mirror was engineered to be resonant at a pure tone (the same tone as was used to create the Lissajous figure) and sand were placed on the mirror being vibrated (at same other tone that created the Lissajous figure) ...then a Chladni pattern would emerge...?
And if so, what would the mathematical relationship be?
To create a lissajou figure you need 2 sinewaves not one.
The plates do resonate at more than one frequency and it is possible to make them resonate at 2 frequencies simultaneously by feeding 2 tones into a loudspeaker.
If you take the example of the basic mode of a square plate, free at the edges (I think you used this eg somewhere) at one frequency the pattern is a cross with nodes at the centre of each face, at a second frequency the pattern is a cross with the nodes at the corners of the plate. If you force the plate to vibrate at both of these frequencies simultaneously you will get a combination of the 2 patterns i.e. 2 superimposed stars.
You could also try building a plate in the same proportion as the lissajou frequencies so that the resonating length/width is the same as the ratio of the sinewaves e.g. 2:1. In this case the rectangular plate pattern is a simple 2 nodes across the width of the plate dividing it into 3 antinodes - the ends go up and the centre goes down etc, this is the same pattern as a rectangular bar. Also this pattern doesn't change with the ratio of width to length unlike the lissajou figure.
The fact is that the lissajou curves and the chladni patterns are 2 different phenomena, giving us different information.
If you want to try applying lissajou curves to qm perhaps you ought to look for related frequencies, say, 2 harmonic oscillators to see whether they exhibit something similar to the curves.
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Offline timey

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Yes Colin - you are on the right track, but let me more fully explain my direction...

The Chladni patterns are already connected to the Schrödinger equation.  Schrödinger used the mathematics of Chladni patterns to work out the atomic orbital of the electron.

The Schrödinger equation is related to the Doppler shift equation via the Lorentz transformations, and perturbations of time are used to calculate the probability of quantum actions.

The common ground in these instances is phase shifting of either space or time.

In that Lissajous patterns can be created by reflected light being vibrating off a mirror, and this is almost synonymous to the Pound Rebka gamma ray emitter being vibrated by frequency tones creating a Doppler shift in the test signal of the experiment - Lissajous figures must have some relationship with the Doppler shift equation and therefore a connection to the gravitational shift equation.

This corresponds with the compound pendulums connection with Lissajous figures because gravity is one of the input sine waves of the compound pendulum.

Lissajous figures also relate to the electron via memoristor and are 'already' connected to quantum.

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Yes - you are entirely correct...  I won't actually be doing this myself because I haven't got a pot to p*ss in and I'd sooner see a dinner on my plate, but yes it would be possible to create a plate that, much like xylophone notes, are engineered to resonate at a pure tone... Inputting that plate with another frequency that is known to create a Lissajous figure when combined with this pure tone, the Chladni pattern that emerges on the plate will not be the same pattern as a the Lissajous figure, but both patterns, in that they are corresponding to the use of the same frequencies, will have a mathematical relationship - and that relationship would be very interesting.

By the physical nature of how the patterns are created, the Lissajous patterns being the result of light thrown outwards into patterns from the extremities of the vibrations, and the Chladni patterns being the result of sand being pushed into the areas of least vibration, the Chladni pattern should, by all logic, be an inverse representation of the corresponding Lissajous figure.
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Offline jeffreyH

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This is the wrong question anyway. How does negative kinetic energy relate general relativity to quantum mechanics?
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Offline timey

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Perhaps, but while not detracting from Dirac's contribution, on the basis that the knee bone is connected to the thigh bone, the question could also be a lot of things, the most direct form of which being: Can quantum and the standard model be united with gravity?

I notice that nobody has commented to confirm or deny my observations on the difference between the physical mechanics creating these patterns...

Never mind or not the notion of 'how' a Chladni plate pattern is created, just 'what' the pattern is and the mathematics of the points of least vibration, I would have thought that it wouldn't be that much of a mathematical venture to analyse Lissajous patterns as to the points of least vibration on the basis that the pattern is being created from the points of most vibration?
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Offline alancalverd

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The coincidence of mathematical models does not necessarily indicate any fundamental connection between the phenomena they model. Tide tables look like (indeed are) multiple superpositions of sine waves and the Southampton tide in particular looks like a simple Lissajous figure as the primary Atlantic tide is modulated by the Isle of Wight, but you'd have a hell of a job predicting it from the shape of hydrogen bonds in seawater.

The use of a sine wave drive in the Pound-Rebka experiment has nothing to do with resonance or interference in the loudspeaker cone - almost the opposite. If you apply a drive current I = a sin(ft) where a is the amplitude and f is a frequency within the linear single mode response of the cone (i.e a low frequency), the velocity of the cone at any time t is a cos (ft). If you use a phase-sensitive detector to correlate the received signal with I you can find the value of t that produces maximum signal and hence calculate the critical Doppler velocity.

The universe is made up of zillions of things (some of which we have never observed) all interacting with each other in umpteen ways (some of which we don't understand). Physics equations rarely invoke more than sine waves and x^2, so they tend to be a bit repetitive: representing the entire orchestra, choir and cathedral acoustics with one bar of dots doesn't equate Lloyd Webber with Haydn.   

When you do succeed, I will of course be delighted to have that sentence quoted in your Nobel speech, but if I wanted to produce a predictive model of quantum gravity, I wouldn't start with Doppler or Chladni.
« Last Edit: 10/10/2016 13:08:17 by alancalverd »
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Offline Colin2B

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I notice that nobody has commented to confirm or deny my observations on the difference between the physical mechanics creating these patterns...
Sorry, been very busy for other than short answers. Will respond when I get a moment.
Need to continue in new theories as your posts have moved a long way over there.

Edit - aAlan responded while I was typing, but my thoughts are similar. I'll try to go through later.
« Last Edit: 10/10/2016 08:27:50 by Colin2B »
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I notice that nobody has commented to confirm or deny my observations on the difference between the physical mechanics creating these patterns...
Sorry, been very busy for other than short answers. Will respond when I get a moment.
Need to continue in new theories as your posts have moved a long way over there.

Edit - aAlan responded while I was typing, but my thoughts are similar. I'll try to go through later.
Hey Colin - no need for apology.

Actually the question "Can quantum and the standard model be united with gravity?" ...is older than I am, but New Theories is OK with me.

http://www.physicsclassroom.com/class/sound/Lesson-4/Standing-Wave-Patterns

It clearly states in this link that all objects resonate with their own natural frequency or frequencies.  That it is driving these natural frequencies with an outside source that causes standing waves.  That the patterns are only created within the medium at specific frequencies of vibration.  And these specific frequencies are harmonics of the natural frequencies of the object.

Therefore since 1 frequency is being driven with another frequency, there 'must' be 2 frequencies involved in creating the Chladni pattern.

Is there anybody reading who can agree on this point?
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Offline timey

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The coincidence of mathematical models does not necessarily indicate any fundamental connection between the phenomena they model. Tide tables look like (indeed are) multiple superpositions of sine waves and the Southampton tide in particular looks like a simple Lissajous figure as the primary Atlantic tide is modulated by the Isle of Wight, but you'd have a hell of a job predicting it from the shape of hydrogen bonds in seawater.

The use of a sine wave drive in the Pound-Rebka experiment has nothing to do with resonance or interference in the loudspeaker cone - almost the opposite. If you apply a drive current I = a sin(ft) where a is the amplitude and f is a frequency within the linear single mode response of the cone (i.e a low frequency), the velocity of the cone at any time t is a cos (ft). If you use a phase-sensitive detector to correlate the received signal with I you can find the value of t that produces maximum signal and hence calculate the critical Doppler velocity.

The universe is made up of zillions of things (some of which we have never observed) all interacting with each other in umpteen ways (some of which we don't understand). Physics equations rarely invoke more than sine waves and x^2, so they tend to be a bit repetitive: representing the entire orchestra, choir and cathedral acoustics with one bar of dots doesn't equate Lloyd Webber with Haydn.   

When you do succeed, I will of course be delighted to have that sentence quoted in your Nobel speech, but if I wanted to produce a predictive model of quantum gravity, I wouldn't start with Doppler or Chladni.

Alan - It is a text book fact that Schrödinger used the mathematics of Chladni patterns to work out the atomic orbital of the electron.  It is also a text book fact that Lissajous patterns have a connection to the electron.  Asking questions of coincidences in physics such as this is not irrelevant, although clearly questions asked may turn out to be irrelevant.  However, without asking the questions one would not know the answers, and even questions being found to have no relevance has relevance in itself.

You said:
"The use of a sine wave drive in the Pound-Rebka experiment has nothing to do with resonance or interference in the loudspeaker cone"

Correct.  Its the actions of the speaker cone vibrating the gamma ray emitter (Pound Rebka), the laser dot on mirror (Lissajous figures),  that cause Doppler shift.

I'm looking at the difference in these Chladni and Lissajous patterns as being due to opposite phase shifting.

Opposite phase shifting becomes relevant to what I am saying with my theory of time and the fact that physics measures physical actions via the standard second, and my theory states the t of any mass situation as being t is equal to the phase period of its f, and any space situation as being t is equal to the phase period of the hypothetical f of the energy of the gravity field at distance from mass.

Much to my disappointment though Alan, my experience with you has led me to the understanding that if it's not already written in a text book, or is not something that yourself and Kibblewhite discussed, then it would seem to be not something that you are capable of considering without prejudice.

So Chladni patterns and Doppler shift is not where you would start in a quest to unite quantum with gravity...  Just for the record, where exactly did "you" start from then?
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Offline alancalverd

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There is no essential connection between Lissajous and Doppler. Your connection between Lissajous and the electron would be interesting to discover. Whatever you do in science, don't confuse the mathematical model with the reality - especially if the model is continuous and the reality is quantised.
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Offline Colin2B

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It clearly states in this link that all objects resonate with their own natural frequency or frequencies.  That it is driving these natural frequencies with an outside source that causes standing waves.  That the patterns are only created within the medium at specific frequencies of vibration.  And these specific frequencies are harmonics of the natural frequencies of the object.
That's the point ive been trying to make all along. It is the sum of these harmonics that causes the standing waves. You don;t need a second frequency, and the outside source doesnt need a frequency component - think blowing across the top of a bottle, yiu are only blowing not whistling or huming a frequency. You may have missed what I was saying or Im not explaining clearly enough.
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Offline timey

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There is no essential connection between Lissajous and Doppler. Your connection between Lissajous and the electron would be interesting to discover. Whatever you do in science, don't confuse the mathematical model with the reality - especially if the model is continuous and the reality is quantised.
Light bouncing off a mirror being vibrated causes a Doppler shift in the light.

Lissajous figures are connected to the electron via memorista.

Whatever you do in science Alan don't confuse a mathematical model with reality, especially if the model is quantised and reality is continuous!
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Offline timey

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It clearly states in this link that all objects resonate with their own natural frequency or frequencies.  That it is driving these natural frequencies with an outside source that causes standing waves.  That the patterns are only created within the medium at specific frequencies of vibration.  And these specific frequencies are harmonics of the natural frequencies of the object.
That's the point ive been trying to make all along. It is the sum of these harmonics that causes the standing waves. You don;t need a second frequency, and the outside source doesnt need a frequency component - think blowing across the top of a bottle, yiu are only blowing not whistling or huming a frequency. You may have missed what I was saying or Im not explaining clearly enough.
No Colin - you explain yourself well and I have missed nothing...
You however seem to be missing the fact that an object has an associated energy, or energies, and that energy has an associated frequency.  And that any energy added to an object in any fashion has an associated frequency.  Some methods of adding energy such as being hit singularly with a rubber mallet will only change amplitude if more energy is given to the force of the strike, but adding energy that consists of an increasing frequency will cause changes in standing waves confined within the object.

Any change in an objects behaviour due to an energy input is an interaction between the energy of the input, and the energy or energies of the object.

Therefore there is the frequency or frequencies of the object, and the frequency of the input signal at play in the creation of Chladni patterns, surely...

How can one logically deduce otherwise?
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Offline alancalverd

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Assuming you mean memristor, I'd appreciate a reference to how they connect electrons to Lissajous figures. Curious devices, they seem to have disappeared from sight in the last 40 years.

Quote
You however seem to be missing the fact that an object has an associated energy, or energies, and that energy has an associated frequency.
Alas that is not true or even generally meaningful.

And, sadly, the Lissajous figures created by reflecting light from a vibrating mirror have nothing to do with Doppler shift. It's just the path of the reflected beam when the mirror rotates about two axes.   

 
« Last Edit: 10/10/2016 22:44:14 by alancalverd »
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Offline jeffreyH

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Fixation on the Einstein papers is a good definition of OCD.

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Offline timey

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Assuming you mean memristor, I'd appreciate a reference to how they connect electrons to Lissajous figures. Curious devices, they seem to have disappeared from sight in the last 40 years.

Quote
You however seem to be missing the fact that an object has an associated energy, or energies, and that energy has an associated frequency.
Alas that is not true or even generally meaningful.

And, sadly, the Lissajous figures created by reflecting light from a vibrating mirror have nothing to do with Doppler shift. It's just the path of the reflected beam when the mirror rotates about two axes.   

https://en.wikipedia.org/wiki/Lissajous_curve

quote:
"A Lissajous curve is used in experimental tests to determine if a device may be properly categorized as a memristor."

https://en.wikipedia.org/wiki/Memristor#Experimental_tests_for_memristors

please see: experimental tests for memristor

Quote:
"Chua and his student Sung Mo Kang generalized the theory of memristors and memristive systems including a property of zero crossing in the Lissajous curve characterizing current vs. voltage behavior."

https://learn.sparkfun.com/tutorials/voltage-current-resistance-and-ohms-law

"The three basic principles for this tutorial can be explained using electrons, or more specifically, the charge they create: Voltage is the difference in charge between two points. Current is the rate at which charge is flowing. Resistance is a material's tendency to resist the flow of charge (current)"

https://prezi.com/k67jmml5iopb/applications-of-lissajous-figures/

I did not watch this as it will not play on my phone, but the write up says: 
"with very difficult math approach like Hamiltonian in Quantum mechanics"

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All mass is made of atoms, which contain electrons, which have energy.

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Ah, ok...good, good!  Not a Doppler shift.  Lets examine that.  The Pound Rebka attaches a gamma ray to a speaker cone and a Doppler shift is created in the test signal of the experiment.  If we attach a laser to the speaker cone then a Doppler shift would be created in the light of the laser.  So by pointing a laser at a mirror attached to a speaker cone, and pointing a laser 'straight' at it the light shining back would be Doppler shifted...

...But the Lissajous pattern is not created like this.  Looking at the tuning fork version, the laser beam  is pointed at a mirror set up at an angle that reflects the beam to another tuning fork with a mirror on it, that then reflects the beam onto the screen.  Both tuning forks are vibrating.  Both mirrors are adding a Doppler shift to the beam of laser light.

« Last Edit: 11/10/2016 01:33:42 by timey »
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Offline timey

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There may be a confusion with phonons.

https://en.m.wikipedia.org/wiki/Phonon

Interesting.  I'll be reading that closely.
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Offline jeffreyH

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And try going to this web site and watch the video to see how the Chladni patterns relate to quantum mechanics. http://oyc.yale.edu/chemistry/chem-125a/lecture-9
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Offline Colin2B

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There may be a confusion with phonons.

I agree Jeff, there is a big difference between the propagation of sound across a crystal lattice and the response of that lattice to mechanical distortion as in the Chladni plates. If we want to estimate the speed of sound in a material, we don't need to do an analysis of the atomic structure of the crystal lattice, we can use Youngs Modulus. I think there is also some confusion with phenomena like black body radiation:
You however seem to be missing the fact that an object has an associated energy, or energies, and that energy has an associated frequency.  And that any energy added to an object in any fashion has an associated frequency. 
There is no direct relationship between increasing the energy input and the resonant frequencies, in fact the resonances require less energy for a particular amplitude of vibration compared to none resonant frequencies. This is similar to the energy wells found in quantum models and that electrons find it easier to remain in certain orbitals.

adding energy that consists of an increasing frequency will cause changes in standing waves confined within the object.
In its quiescent state there are no flexing movements in the plate so no standing waves 'confined' in the plate.

Therefore there is the frequency or frequencies of the object, and the frequency of the input signal at play in the creation of Chladni patterns, surely...

How can one logically deduce otherwise?
As I explained earlier, the input frequency acts in the same way as hitting with a hammer, causing  a mechanical displacement, the returning force due to stiffness and the mass of the plate determines the resonance, hence the harmonics, hence the patterns. This is all due to the flexing of the plate and there is no underlying frequency which the input signal combines with.

This corresponds with the compound pendulums connection with Lissajous figures because gravity is one of the input sine waves of the compound pendulum.
No, there is no gravity sinewave. Gravity acts as the returning force, in the same way as the stiffness of the plate.

By the physical nature of how the patterns are created, the Lissajous patterns being the result of light thrown outwards into patterns from the extremities of the vibrations, and the Chladni patterns being the result of sand being pushed into the areas of least vibration, the Chladni pattern should, by all logic, be an inverse representation of the corresponding Lissajous figure.
As Alan said, the lissajous patterns are the locus of the sum of 2 sine waves, as such they will be the resultant of nodes and antinodes of the individual waves.

If you are going to draw parallels between mechanical phenomena an atomic/quantum behaviour you need to start with a correct model of the mechanical system.
« Last Edit: 11/10/2016 10:08:40 by Colin2B »
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Offline evan_au

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As an aside...
Quote from: alancalverd
memristor.... Curious devices, they seem to have disappeared from sight in the last 40 years.
Research is still continuing - the latest fads seem to be in emulating neurons, or displacing flash drives...
See: http://spectrum.ieee.org/the-human-os/semiconductors/memory/mimicking-the-synapses-of-the-brain

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Offline timey

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There may be a confusion with phonons.

I agree Jeff, there is a big difference between the propagation of sound across a crystal lattice and the response of that lattice to mechanical distortion as in the Chladni plates. If we want to estimate the speed of sound in a material, we don't need to do an analysis of the atomic structure of the crystal lattice, we can use Youngs Modulus. I think there is also some confusion with phenomena like black body radiation:

But I am not discussing the propagation of sound - I am discussing the distribution of resonant vibration.

Phonons are the product of perturbation theory as are all quantum calculations.  I'm not sure what confusion you refer to regarding the black body radiation phenomenon, but fact of the matter is that if one attempted to apply these time perturbations to the black body radiation data directly, then the quantised nature of the data would be eliminated at source.

You however seem to be missing the fact that an object has an associated energy, or energies, and that energy has an associated frequency.  And that any energy added to an object in any fashion has an associated frequency. 
There is no direct relationship between increasing the energy input and the resonant frequencies, in fact the resonances require less energy for a particular amplitude of vibration compared to none resonant frequencies. This is similar to the energy wells found in quantum models and that electrons find it easier to remain in certain orbitals.
adding energy that consists of an increasing frequency will cause changes in standing waves confined within the object.
In its quiescent state there are no flexing movements in the plate so no standing waves 'confined' in the plate.

The standing waves that are inherent in the plate are holding it in its non-vibrating position.  Without them the plate would not be a plate.

Therefore there is the frequency or frequencies of the object, and the frequency of the input signal at play in the creation of Chladni patterns, surely...

How can one logically deduce otherwise?
As I explained earlier, the input frequency acts in the same way as hitting with a hammer, causing  a mechanical displacement, the returning force due to stiffness and the mass of the plate determines the resonance, hence the harmonics, hence the patterns. This is all due to the flexing of the plate and there is no underlying frequency which the input signal combines with.

Well actually Colin, you have explained this scenario in both ways.  You have told me that a plate has natural frequencies, and the input to the plate has no frequency, in that one blows rather than whistles across the top of a bottle to create a sound, or hits with a hammer,(bowing with a violin bow is actually much more complicated physics)....
And then you tell me, as we can quite clearly observe in the links provided, that Chladni patterns are forming on a plate and changing from one pattern to another as an input is being increased in its frequency.

How the different tones on steel drums are constructed and how the standing wave of this tone resonating is confined to the tone zone is interesting Colin.   

This corresponds with the compound pendulums connection with Lissajous figures because gravity is one of the input sine waves of the compound pendulum.
No, there is no gravity sinewave. Gravity acts as the returning force, in the same way as the stiffness of the plate.

Gravity is one of the driving forces of the compound pendulum's representation of a Lissajous figure.

By the physical nature of how the patterns are created, the Lissajous patterns being the result of light thrown outwards into patterns from the extremities of the vibrations, and the Chladni patterns being the result of sand being pushed into the areas of least vibration, the Chladni pattern should, by all logic, be an inverse representation of the corresponding Lissajous figure.
As Alan said, the lissajous patterns are the locus of the sum of 2 sine waves, as such they will be the resultant of nodes and antinodes of the individual waves.

Precisely the connection that I am making with Chladni plates.
 
If you are going to draw parallels between mechanical phenomena an atomic/quantum behaviour you need to start with a correct model of the mechanical system.

My post to Alan concerning the tuning fork version of producing Lissajous patterns 'is' mechanically correct.
« Last Edit: 11/10/2016 12:47:54 by timey »
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Offline timey

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Jeff - thanks for the links...

Please see first part of post to Colin above.

Please also see the 2014 link of applications of Lissajous figures in my last post to Alan, and the notion of maths approaching the Hamiltonian.

https://en.wikipedia.org/wiki/Quantum_gravity

quote:
" The Problem of Time
Main article: Problem of Time
A conceptual difficulty in combining quantum mechanics with general relativity arises from the contrasting role of time within these two frameworks. In quantum theories time acts as an independent background through which states evolve, with the Hamiltonian operator acting as the generator of infinitesmal translations of quantum states through time.[29] In contrast, general relativity treats time as a dynamical variable which interacts directly with matter and moreover requires the Hamiltonian constraint to vanish,[30] removing any possibility of employing a notion of time similar to that in quantum theory."
unquote:

Please note that Special Relativity also uses an independent time background.

Please note that the Shrodinger and Doppler shift are united in quantum via the Lorentz transformations, which phase both time and space.
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Offline jeffreyH

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Then what is required, as I have stated in new theories, is a concept of action dilation rather than just time dilation. Then time is no longer an independent background in quantum mechanics.
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Offline alancalverd

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Yes, since a Lissajous figure is simply a plot of x = a sin ft against y = b sin (f't + p) where a and b are amplitudes, f and f' are frequencies, and p  is a phase angle, it's quite a handy tool for looking at the behavior of nonlinear systems.

There was (maybe still is) a suggestion that memristors could form useful oscillators, in which case f = f' and the Lissajous figure can show the phase relationships around the tuned circuit. No big deal: we use L f 's for synchronising all sorts of things from atomic clocks to aircraft engines. 
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Offline alancalverd

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Ah, ok...good, good!  Not a Doppler shift.  Lets examine that.  The Pound Rebka attaches a gamma ray to a speaker cone and a Doppler shift is created in the test signal of the experiment.  If we attach a laser to the speaker cone then a Doppler shift would be created in the light of the laser.  So by pointing a laser at a mirror attached to a speaker cone, and pointing a laser 'straight' at it the light shining back would be Doppler shifted...

...But the Lissajous pattern is not created like this.  Looking at the tuning fork version, the laser beam  is pointed at a mirror set up at an angle that reflects the beam to another tuning fork with a mirror on it, that then reflects the beam onto the screen.  Both tuning forks are vibrating.  Both mirrors are adding a Doppler shift to the beam of laser light.

I see your confusion. The Lissajous figure is, as I said above, just the path of a light beam, particle or whatever that moves cyclically in the x and y directions simultaneously. To get a Doppler shift you need to move the source in the z direction, i.e. along the direction of propagation of the signal, which is what P&R did. You can do this in principle with a laser and a vibrating mirror but the Doppler shift is so small that it would be lost in the normal bandwidth of the laser. The trick with P&R was to use a Mossbauer filter which has an incredibly narrow bandwidth. I'll leave the numbers up to you, as you have the Doppler equation and at least as much experience of tuning forks as I have!

True story. My first day as a physics laboratory demonstrator brought me into contact with a student  who was indeed working with (but not entirely understanding) Lissajous figures. Her experimental writeup was "different patterns were obtained by fiddling with various knobs on the oscilloscope". I gave her full marks because she had written down exactly what she did and what she saw (the essence of experimental science) whilst the other students had merely copied the method scripts that I had written and put in a few plausible numbers. A few years ago she was awarded "Physics Teacher of the Year" by the Institute of Physics.
« Last Edit: 11/10/2016 23:29:52 by alancalverd »
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Offline Colin2B

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But I am not discussing the propagation of sound - I am discussing the distribution of resonant vibration.
Sorry, I thought for a moment you were suggesting that the standing soundwaves in the plates have discrete energies associated with their frequencies. I should have realised that you would understand  why this is meaningful for v high frequencies eg light, but not for those of sound.

The standing waves that are inherent in the plate are holding it in its non-vibrating position.  Without them the plate would not be a plate.
I assume that as above you are not talking about the standing sound waves in the plate, because those standing soundwaves which form the chladni patterns do not form and have no existence until the plate is stimulated to vibrate either by hammer, bow or frequency from a loudspeaker. The standing waves are the resonance we hear. The plate is still a plate without those standing waves, so I'm confused about which standing waves are holding the plate in its nonvibrating position.

Well actually Colin, you have explained this scenario in both ways.  You have told me that a plate has natural frequencies, and the input to the plate has no frequency, in that one blows rather than whistles across the top of a bottle to create a sound, or hits with a hammer,(bowing with a violin bow is actually much more complicated physics)....
And then you tell me, as we can quite clearly observe in the links provided, that Chladni patterns are forming on a plate and changing from one pattern to another as an input is being increased in its frequency.
That's because, as I have explained, there are a number of different ways in which the plates may be stimulated, I agree that the bow is more complicated physics, but at the level we are discussing here it is still just another way of stimulating the different modes of resonance. But the point I have been trying to make is there is no inherent wave (standing or otherwise) which combines with another input frequency to create the patterns, the patterns are only the result of the resonance, standing soundwaves and their harmonics, which superpose onto each other.
You cannot draw a parallel between the chladni patterns and the lissajou figures and argue that they are the result of 2 frequencies. What is an interesting parallel is that the more interesting lissajous figures occur when the 2 frequencies have integer relationships. This is precisely what is happening with the chladni patterns as the harmonics are all integer multiples, the difference is that whereas lissajous is made from only 2 frequencies, chladni often have at least 6 frequencies in each vibrating length, so 12 for square/rectangle.

Gravity is one of the driving forces of the compound pendulum's representation of a Lissajous figure.
Agreed, however, gravity is not an input sinewave as you stated, the gravitational force is constant.

I'm not sure whether any further input from me will help rather than hinder your quest to link schrödinger, Doppler and lissajous, because such input would be based on sound propagation rather than quantum level. For example, we could discuss how when a violin string resonates it pushes against the bow making it slip across the strings at the resonant frequency, a similar effect occurs when blowing across a tube where the vortices which initiate the resonance are forced to follow the resonant frequency, but I can't see how such facts, fascinating as they are, can help you solve your problems at a quantum level.
Best of luck in your quest.
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Offline timey

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That is a lovely story Colin.

(Edit: Just realised that should be 'lovely story Alan' and that the next 2 paragraphs are in answer to your post that I mistakenly thought Colin had posted)

The only part of the Pound Rebka experiment that interests me is the part where they say: When the Doppler shift of the test signal was of the correct type to be 'matched and cancelled out', the gamma ray was then able to be received by the receiver.

The only part of the Lissajous patterns that interests me is the 'outward' gyrations and inertias in relation to frequency and the fact that a change in mass or a change in gravity will affect the gyration and inertia of a Lissajous pattern being created by a compound pendulum.

Let's try a different tack.  A Chladni plate pattern is caused at the points of least vibration.  Now imagine that the sand was being pushed to the points of most vibration instead.  Would this be a Lissajous pattern?

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(Edit: and to Colin's post)

Edit: Aww, just read your latest post.  Yes blowing over a bottle top or flute is really interesting and the physics are complicated because you can change the octave of a tone by changing the shape of your mouth and the way you blow.  Much the same as the wrist and pressure action of a violin bow.  Might have to open a whole new thread for that one Colin.  I know by experience how to facilitate these effects in both flute and violin, but could learn a lot about the why of it :)...
« Last Edit: 12/10/2016 16:47:24 by timey »
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Offline timey

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Then what is required, as I have stated in new theories, is a concept of action dilation rather than just time dilation. Then time is no longer an independent background in quantum mechanics.

Well Jeff, one is free to entertain trains of thought.  I'm not quite sure what you mean by dilated action.  The equivalence principle denotes that each reference frame must be the physical equivalent of all other reference frames.

In stating time as variable in the quantum region at the stage of the blackbody data that produced Planck's h constant in the manner that I have suggested on your new theories thread, where... as the frequency is observed to be increasing, the length of the standard second is decreased so that the Planck data curve matches the Jean Reiliegh classical curve of the ultra violet catastrophe.  Then the quantised nature of the data will become linear.

We don't need to talk in terms of quantum from that point on.

This concept does however force one into several physical cul de sacs, all of which lead to the model I describe on new theories.

But for this board:

The consequences of different reference frames running at variable rates of time gives rise to the question of simultaneity and a universally constant present. 

On the basis that it would be acceptable to discuss the concept of quantum states being multiverses comprised of copies of this universe displaying the actions of what happens on the other side of Schrödinger's partitioned box, I think I can be forgiven for discussing the possibility that variable rates of time can occur simultaneously to each other, ie: side by side, and that a logical solution to maintaining the universally constant present within this construct is that our observation of reference frames of rates of time differing from our own are time frame dependent and proportional to the difference in rate of time of observation point and rate of time at point of observation.

This concept becomes interesting when considering the Bekenstien, Hawking black hole conundrum, the second law of thermodynamics and the energy conservation law.
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Offline jeffreyH

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If we are in reference frame A and we are observing the action of a particle in reference frame B along a line element, how is that different to observing a change in relativistic mass? It is only a change in our viewpoint of the time component that makes the difference. Isn't it time that prevents a union between QM and GR?
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Offline timey

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Well its kind of hard for me to get into the discussion of relativistic mass without straying into New Theories territory, but if you think about the implications of matching the Planck data curve to the Jean Rayliegh classical curve by decreasing the length of a standard second as frequency is increased, then you will realise that frequencies in the lower registers may require that the standard second is increased in length.

By attributing open space with a time dilation of its own that decreases the length of a second as the gravity field decreases in strength with distance from mass...

Looking at this concept of the rate of time getting slower for 'space' in relation to clocks slowing in relative motion, you will find that the necessity for relativistic mass has been rendered redundant. The universal speed limit of the speed of light is upheld as well as the equivalence principle, in that light will always travel 299 792 458 metres per second, whatever the length of that second is, the speed you travel will always be a percentage of the reference frames speed of light as per the reference frame that is being travelled through's length of second, this percentage of the speed of light you are travelling will affect your motion related slowing of time, and that the interplay of both phenomenin in relation to each other ensures that mass never achieves the speed of light of the reference frame it is travelling through, and that it is gravity potential that is the mechanical function of frequency changes for mass travelling through space.

This then forces one to look at other means of calculating what is happening with light in the gravity field, and seek an alternate perspective concerning calculating kinetic energy with respect to relative motion related slowing of time.
« Last Edit: 12/10/2016 17:00:55 by timey »
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Offline alancalverd

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Let's sum up the Lissajous stuff. Any periodic shape can be synthesised or approximated by the addition of sine waves.   A Lissajous figure is the result of vector addition of two periodic functions at right angles. That's all there is to it.
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Offline timey

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Great stuff Alan!

But could you please tell me what the maths of an inverse representation of a Lissajous figure are, what the maths for an inverse representation of a Chladni plate are, and if the inverse representation of each relates mathematically to the non inverse representation of the other?
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Offline Colin2B

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Let's try a different tack.  A Chladni plate pattern is caused at the points of least vibration.  Now imagine that the sand was being pushed to the points of most vibration instead.  Would this be a Lissajous pattern?
It would still be a Chladni pattern, it wouldn't be a lissajous pattern.
Chladni patterns are just a mapping of the nodes and antinodes of a plate and it just happens that the easiest way to visualise them is by indicator gathering in the nodes, It is possible to display the antinodes pattern using a form of laser holography which shows the areas of maximum displacement as dark areas.
I can't get some maths symbols to post otherwise I would show you the maths, but lissajou patterns are the locus (movement of a point) resulting from 2 sinewaves one pushing the point in the x direction and the other in the y direction (as Alan said), whereas the wavefunction for the Chladni patterns of a rectangular plate with free edges is the product of 3 cosine functions and is stationary. Because lissajous are motions of a point and Chladni patterns are stationary it doesn't make sense to talk of one being the inverse of the other.
Interesting aside, Faraday discovered that very light material e.g. fragments of bow hair, tended to move to the antinodes drawn there by surface air currents caused by the flexing of the plate.

Edit: Aww, just read your latest post.  Yes blowing over a bottle top or flute is really interesting and the physics are complicated because you can change the octave of a tone by changing the shape of your mouth and the way you blow.  Much the same as the wrist and pressure action of a violin bow.  Might have to open a whole new thread for that one Colin.  I know by experience how to facilitate these effects in both flute and violin, but could learn a lot about the why of it :)...
Yes, overblowing has its parallel in bow technique, and it really brings out an understanding of the differences between sympathetic resonances and stimulated resonance, but as you say separate subject. Also, there is limited time and space to cover these subjects fully so it would have to be a very superficial discussion like the one we've had on Chladni where we haven't even scratched the surface.

Just as an aside before we leave this. Phonons were mentioned and these as you are aware don't play a part in chladni patterns. For others reading this, phonons propagate by longitudinal and transverse displacement of atoms in the material lattice, but because these displacements are extremely small the amplitudes of the waves are also small, in fact almost inaudible. Plate vibrations on the other hand have large displacements and can produce  very loud sounds (wouldn't have string instruments otherwise - well maybe electric bass), this is because the standing waves are caused by the plates bending and twisting rather than relying on longitudinal or transverse waves through the plate.
and the misguided shall lead the gullible,
the feebleminded have inherited the earth.