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could there be a relationship between [Chladni] node patterns and lissajous curves?

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.

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.

do you think a Chladni plate pattern is involving 2 frequencies, like the Lassijous figures do, or is it just 1 frequency?

isn't stating the bowing adding an energy to the situation in as much as saying the bow is adding a frequency?

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?

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.

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.Quote from: Colin2B on 05/10/2016 17:03:25Schrodinger? 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:...sorry, you cannot view external links. To see them, please REGISTER or LOGINQuote:" 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?

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?

What you are saying here is not really correct. Please see link:...sorry, you cannot view external links. To see them, please REGISTER or LOGINQuote:" 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:

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/n^{2}, so the harmony could be described at best as "complex", but most people would just call it "noise".

..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?

QuoteA 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.

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

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?

...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.

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

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?

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

Quote from: timey on 09/10/2016 18:30:55I 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.

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.

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.

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.

Quote from: timey on 10/10/2016 13:14:25It 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.

You however seem to be missing the fact that an object has an associated energy, or energies, and that energy has an associated frequency.

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.QuoteYou 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.

There may be a confusion with phonons....sorry, you cannot view external links. To see them, please REGISTER or LOGIN

There may be a confusion with phonons.

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.

adding energy that consists of an increasing frequency will cause changes in standing waves confined within 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?

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

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.

memristor.... Curious devices, they seem to have disappeared from sight in the last 40 years.

Quote from: jeffreyH on 11/10/2016 00:22:32There 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:

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.

In its quiescent state there are no flexing movements in the plate so no standing waves 'confined' in the plate.

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.

No, there is no gravity sinewave. Gravity acts as the returning force, in the same way as the stiffness of the plate.

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.

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.

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

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.

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.

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

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.

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?

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 ...