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Author Topic: Can this relationship be derived between Schrodinger equation and Doppler shift?  (Read 13116 times)

Offline Colin2B

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If there were 2 light beams what you are saying would be correct. 
It works for one beam and 2 mirrors, you really arn't getting this are you. Sit down and think it through.

Now Colin - a thought experiment.  If we simply shine a static line of light onto the second mirror, ie: a line of light that is not being created by wobbling a dot of light, and then wobble the second mirror, will the second mirror turn this static line of light into a circle?  Or any other Lissajous figures?
Why should it?
The whole point of this is that what you see on the screen is the resultant of 2 sinewaves projected onto the screen by the 2 mirrors. If you only have one mirror and one tuning fork (i.e. one sinewave) you don't get the patterns.

I don't know if this helps but here is an example of doing the trig using graph paper, which is what I meant by drawing it out. http://www.intmath.com/trigonometric-graphs/7-lissajous-figures.php
 

Offline timey

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Colin - I've always had a nice time with you online, so tucking my sensitive soul back into top pocket, I'm going to ignore the rather hurtful tone of your recent posts.

My contention with your post was that you said that a Lissajous figure is the result of 2 laser dots combining on a screen.  Its not 2 dots, its 1 dot vibrated into a line, that is then vibrated into a pattern.

Thank you for the link.  Please excuse me if I am wrong, but the maths portrayed are describing the dimensions of the Lissajous pattern itself.

I am interested in the maths of the physics of the wave periods creating the pattern.

It is because both mirrors are vibrating back and forth that a Lissajous pattern is caused in the beam of light reflected from one vibrating mirror to another vibrating mirror...  In that both mirrors are moving back and forth, albeit the movement of each is at right angles to the other, the distance between both of the mirrors is altered by this movement and constantly changing from long short, or short long - or the distance between the mirrors stays the same but the position of this distance in space is changing from one side to the other and back. (In phase, out of phase)

Are you with me so far?

All of what I describe above are wave periods in themselves.

Can we agree on this?
 

Offline alancalverd

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Quote
you said that a Lissajous figure is the result of 2 laser dots combining on a screen.

No he didn't! Everyone here has said in all sorts of ways that a Lissajous figure is simply the locus of a point that moves cyclically in two dimensions. The most common is the sum of two sine waves in the x and y directions. That's all there is to it.
 

Offline timey

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Yes he did...

So the spot on the screen traces, albeit magnified, the motion of the end of the tuning fork.
With 2 tuning forks the motion on the screen will be a combination of one moving the spot up and down, and the other moving it side to side such that at any point in time it's xy position (coordinates) will be specified by the value derived from the formulae Alan posted.

...and the reality is that the first mirror in line vibrates the spot into a line, and the second mirror vibrates the line into Lissajous figures.   Therefore the relationship of changing distance between the 2 vibrating mirrors has got to be the defining factor.

Now if you are telling me that the formula you provided describes not only the dimensions of the Lissajous figure itself, but also the wave periods of the changes in distance between the mirrors caused by the vibrations, and the wave period that would be apparent if you attached the laser in line to the top of a vibrating tuning fork for a measure of the distance of the back and forth, then I will agree to agree that that is all there is to Lissajous figures.

So what are you telling me?
 

Offline jeffreyH

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Yes he did...

So the spot on the screen traces, albeit magnified, the motion of the end of the tuning fork.
With 2 tuning forks the motion on the screen will be a combination of one moving the spot up and down, and the other moving it side to side such that at any point in time it's xy position (coordinates) will be specified by the value derived from the formulae Alan posted.

...and the reality is that the first mirror in line vibrates the spot into a line, and the second mirror vibrates the line into Lissajous figures.   Therefore the relationship of changing distance between the 2 vibrating mirrors has got to be the defining factor.

Now if you are telling me that the formula you provided describes not only the dimensions of the Lissajous figure itself, but also the wave periods of the changes in distance between the mirrors caused by the vibrations, and the wave period that would be apparent if you attached the laser in line to the top of a vibrating tuning fork for a measure of the distance of the back and forth, then I will agree to agree that that is all there is to Lissajous figures.

So what are you telling me?

If a trained physicist with decades of experience is telling you something it might be at least polite to pay attention.
 

Offline timey

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I've asked a question of said experienced physicist concerning the maths that were posted by that experienced physicist.  A natural response from a non mathematician, and hardly impolite.

The purpose of your post being what?   That you know the answer but just wish to
continue in your position of superiority and make belittling remarks?
 

Offline Colin2B

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Please excuse my 'tone', but it is born of frustration. I've tried to explain this from a number of different angles and I've often had the feeling that you really haven't read, or at least not understood, what I have written. The impression you can give is that I really don't understand what I am talking about. So tucking my sensitive .....

Ok, example of misreading:
My contention with your post was that you said that a Lissajous figure is the result of 2 laser dots combining on a screen.  Its not 2 dots, its 1 dot vibrated into a line, that is then vibrated into a pattern.
Look again at the quote in your reply to Alan:
So the spot on the screen traces, albeit magnified, the motion of the end of the tuning fork.
With 2 tuning forks the motion on the screen will be a combination of one moving the spot up and down, and the other moving it side to side such that at any point in time it's xy position (coordinates) will be specified by the value derived from the formulae Alan posted.
I've emboldened the key words that show I was speaking of one spot. I've also made it clear in other posts that it is one spot.

Thank you for the link.  Please excuse me if I am wrong, but the maths portrayed are describing the dimensions of the Lissajous pattern itself.
It is the locus of the spot over time.
I'm not sure what you mean by dimensions because the figure will be larger or smaller depending on how far away the screen is. The maths shows the locus which traces out the shape. So if by dimensions you mean shape, then yes.

I am interested in the maths of the physics of the wave periods creating the pattern.
That is what the maths shown does.
a and b in the formula represent the frequency of the 2 tuning forks. As Alan explained, the relative frequency and phase of a and b determine the pattern.

It is because both mirrors are vibrating back and forth that a Lissajous pattern is caused in the beam of light reflected from one vibrating mirror to another vibrating mirror...  In that both mirrors are moving back and forth, albeit the movement of each is at right angles to the other, the distance between both of the mirrors is altered by this movement and constantly changing from long short, or short long - or the distance between the mirrors stays the same but the position of this distance in space is changing from one side to the other and back. (In phase, out of phase)

Are you with me so far?
Ok up to the word albeit. Why did you write "albeit the movement of each is at right angles to the other"? The movement has to be at right angles otherwise you would just get a single line.
It's not the changing distance between the mirrors as I explained in an earlier post.
 

Offline jeffreyH

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It is not a case of me knowing the answer. We all know the answer and have been trying to impart it to you. You have chosen to be obstinate and self defeating. Instead why not pick up a book on arithmetic or algebra and start reading. You might have a pleasant surprise. Once you start becoming confident with the mathematics then you won't have these problems. To do otherwise is laziness.
 

Offline timey

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You know Jeff - I've been talking to people on this thread for a year and a half.  I can remember that Colin plays guitar, is interested in outside sound recording, and has either an outsized or undersized woodpile on one side of his garage (unless he's dealt with it since last year)...
You were very ill in hospital last year, you lungs, you have worked as a water flow engineer (or something very similar), you have an intelligent wife, your dad is bigger than Theboxes dad, and your daughter displayed usual behaviour as a child...
What I remember about details of Alan would fill a couple of pages.

Is it so hard for you to remember that I conduct all my internet activity on a small phone screen (that is cracked and constantly freezing up) because my laptop is broken, that my horse and carriage business is far and beyond on the skids, I have no money and both my family and the animals are driven by a powerful need to eat, and time is the payment required to achieve that.  Alternatively animal welfare will take the horses that are too old to sell or re-home, and put them to death.

I am not too lazy to learn maths, I just don't have a natural affinity with the notation and find it hard to visualise the physics of an equation unless it is broken down into words and put into context.

I think it is perfectly acceptable to ask for help, and for clarification of that help when necessary, and that skill sharing is a pleasant ideal.  I have certainly always helped others to understand anything they thought that I might be able to help them with.

I also think it a display of dubious character to ridicule those who one feels are inferior to ones own self, as you clearly feel that I am to you.  But please know, I am not inferior to you, I am different to you, and although I do have a high opinion of my own abilities, I don't have any less high opinion of anyone else's.  I feel that we all have something to offer, and at the other end of the scale, no person can know everything.  Therefore it is just as well people are different from each other, and think about things from different perspectives, because it would be a bloody well boring world if we didn't.

I'm not here to have a my cock is bigger than your cock competition.  I understand and fully admit where and when my understanding is lacking, and know that I sometimes miss use terminology.  But on the basis that you guys are pretty clever, right?
...I merely wish to talk in depth about physics, and the physical experiments of physics, and preferably I'd like to have FUN when I'm doing it. 

Is that too much to ask?

Now what I am asking is if the formula that Alan provided describes the changes in the distance between the vibrating surfaces the light is being reflected off, or if it would be a different formula that describes this...

I'm quite sure that no-one has tried to impart this to me as of yet.
 

Offline timey

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Please excuse my 'tone', but it is born of frustration. I've tried to explain this from a number of different angles and I've often had the feeling that you really haven't read, or at least not understood, what I have written. The impression you can give is that I really don't understand what I am talking about. So tucking my sensitive .....

Ok, example of misreading:
My contention with your post was that you said that a Lissajous figure is the result of 2 laser dots combining on a screen.  Its not 2 dots, its 1 dot vibrated into a line, that is then vibrated into a pattern.
Look again at the quote in your reply to Alan:
So the spot on the screen traces, albeit magnified, the motion of the end of the tuning fork.
With 2 tuning forks the motion on the screen will be a combination of one moving the spot up and down, and the other moving it side to side such that at any point in time it's xy position (coordinates) will be specified by the value derived from the formulae Alan posted.
I've emboldened the key words that show I was speaking of one spot. I've also made it clear in other posts that it is one spot.

Thank you for the link.  Please excuse me if I am wrong, but the maths portrayed are describing the dimensions of the Lissajous pattern itself.
It is the locus of the spot over time.
I'm not sure what you mean by dimensions because the figure will be larger or smaller depending on how far away the screen is. The maths shows the locus which traces out the shape. So if by dimensions you mean shape, then yes.

I am interested in the maths of the physics of the wave periods creating the pattern.
That is what the maths shown does.
a and b in the formula represent the frequency of the 2 tuning forks. As Alan explained, the relative frequency and phase of a and b determine the pattern.

It is because both mirrors are vibrating back and forth that a Lissajous pattern is caused in the beam of light reflected from one vibrating mirror to another vibrating mirror...  In that both mirrors are moving back and forth, albeit the movement of each is at right angles to the other, the distance between both of the mirrors is altered by this movement and constantly changing from long short, or short long - or the distance between the mirrors stays the same but the position of this distance in space is changing from one side to the other and back. (In phase, out of phase)

Are you with me so far?
Ok up to the word albeit. Why did you write "albeit the movement of each is at right angles to the other"? The movement has to be at right angles otherwise you would just get a single line.
It's not the changing distance between the mirrors as I explained in an earlier post.

Ah Colin - just saw your post, and I take on board your underlining of emphasis as pointed out, and can say I was mistaken in my interpretation...

It may look as though I am not reading through because I do not answer each point in multi quotes.  It takes hours to create them on this phone screen, so much as I'd like to, I don't have time.  I just pick the most relevant bits.

So if a) is one frequency, or sine wave, and b) is the other, ie: tuning fork 1 and tuning fork 2, can we now look at the phase that you refer to?  What in the physical experiment represents phase?

(edit: we can come back to the angle the beam of light hits the mirrors at after)
« Last Edit: 18/10/2016 04:00:55 by timey »
 

Offline alancalverd

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The distance between the tuning forks is irrelevant. What matters is the angular deflection of the beam in the x and y directions. The separation has to be small enough (or the mirrors large enough) that the beam reflected off the first mirror is always intercepted by the second mirror, but that's it.
 

Offline timey

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I realise Alan that the length of distance that the tuning forks are 'set up' apart is irrelevant, apart from the image created by the back and forth of the first mirror fitting onto the second mirror...
It is the miniscule changes in this set up distance caused by the back and forth motions of the mirrors that I'm referring to.
 

Offline alancalverd

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That will induce a minuscule asymmetry of the Lissajous figure. So?   
 

Offline timey

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So - do the maths you provided describing the geometry of a Lissajous figure also describe this asymmetry, or would describing this asymmetry of the Lissajous figure require a different set of maths?
 

Offline alancalverd

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I think you would just add a small constant to one of the sine waves, but now I'm having difficutly even imagining the optical path!
 

Offline jeffreyH

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I think you would just add a small constant to one of the sine waves, but now I'm having difficutly even imagining the optical path!

Maybe you need to revise a little trigonometry. And no don't mention equilateral triangles.
 

Offline timey

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I think you would just add a small constant to one of the sine waves, but now I'm having difficutly even imagining the optical path!

Yes...(chuckle)...  It's beyond mind boggling trying to imagine the the optical light path creating the circle, let alone more complex patterns...

The changes in the 'set up' distance between the mirrors is phase dependent...

Hit both tuning forks at same time from the left side, and we have the 'set up' distance rocking back and forth in space right to left...
Hit both tuning forks at the same time from the right side, and we have the 'set up' distance rocking back and forth in space left to right...
Hit both tuning forks at the same time, 1 to the left, 1 to the right, from the internal orientation, and the 'set up' distance changes, rocking from longer, shorter...
Hit both the tuning forks at same time, 1 to right, 1 to left, from outside orientation, and the 'set up' distance changes, rocking from shorter, longer...

...the changes in distance between the mirrors are then vastly complicated by the orientation of the movement of the mirrors being at right angles.  This in effect adds another dimension of long short, short long, and rocking of distance in space from right to left, or left to right.
 

Offline Colin2B

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So if a) is one frequency, or sine wave, and b) is the other, ie: tuning fork 1 and tuning fork 2, can we now look at the phase that you refer to?  What in the physical experiment represents phase?
It is the relative phase of the 2 sinewaves.
In the double pendulum you can start them together or with any phase relationship you want.
With the tuning forks starting them with a specific phase relationship will be tricky as the common way of starting is by tapping it and, as you will never get the timing exact, the phase will be random.
However, it's not too critical, it is unlikely you will hit exactly inphase or at pi so if f1=f2 you are unlikely to get straight lines, neither are you likely to get a perfect circle, an ellipse is the most likely.

I notice you are asking Alan if the maths he described covers the change of distance between the forks. The thing to consider is that the maths describes perfect lissajous curves (produced mathematically) and any mechanical system will introduce some imperfections.
For eg I had a think about the double pendulum and reckon there are at least 3 imperfections:
- the sand comes out at a constant rate but pendulums have their max speed at the bottom of swing and minimum at the ends, so the thickness of sand will change making the line slightly wider in places.
- the sand also has inertia so at the ends of the swing I think it will overshoot slightly distorting the curves.
- the pendulum doesn't trace a path parallel to the surface, so some distortion will result.
Also, if the system uses a pen rather than sound there will be friction that affects the curves. I'm sure you can think of others.

The tuning fork/mirror system doesn't introduce much distortion, Alan is typically understating when he says minuscule as it is far less than that. I won't spoil your fun by telling you what I think it is, but to aid your calculations, the amplitude of the tuning fork can be taken as 1mm and you don't have to do all the combinations for the 2 forks, just the bounding conditions will give you the range of the effect.
When you've concluded that it is irrelevant to discussion on lissajous curves let me know.

 

Offline timey

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The phase between the sine waves is physically represented in the changes of position of the set up distance in the surrounding space, or changes in the distance of the set up distance between the mirrors...

Yes these changes in distance are minuscule, but they are the distances that the light beam travels and these miniscule differences are what is amplified by the distance between the second mirror and the display screen.  If not for this amplification, what we would observe would be too miniscule to properly discern.

You are correct, this discussion is not concerning Lissajous figures, it is concerning the distribution of resonant vibrations.  It's what's happening between the mirrors that interests me, not what is occurring on the screen.

Evan made a post earlier this thread explaining how a singular mirror on an axis can be driven to creating Lissajous figures.  The phasing between the sine waves occurs on 1 mirror moving in 3 dimensions.
« Last Edit: 19/10/2016 01:23:18 by timey »
 

Offline alancalverd

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OK let's have another go at the tuning forks. Assume the first one produces a perfect sinusoidal oscillation in the x direction. This is amplified by the distance from the center of oscillation to the final screen. The second mirror would do the same in the y direction but also alters the x amplification because it is altering the length of the optical path from the x mirror.

Of course it isn't the linear displacement that causes the beam to move, it's the angular movement, and this is a fraction of a degree for a tuning fork, so you would probably need a meter or so of optical path to get a visible display. If the amplitude of the fork vibration is 1 mm then the variation in x amplification will be +/-1/2000, almost certainly undetectable and anyway of absolutely no physical significance.

     
 

Offline timey

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OK - stating any amplification of effects as being due to a) the distance between the first mirror in line to the laser beam source and the second mirror, and b) the distance between the second mirror in line to the laser beam source and the screen...

We can now look at the scenario where there is just a singular mirror set up on an axis being driven by 2 sine waves, and the amplification of effect is due only to the distance between this singular mirror and the screen - where clearly these very small movements of the phasing between the sine waves in the mirror are of physical significance, because if they were not occurring, a Lissajous figure would not be reflected onto the screen...

The axis provides the mirror with 3 dimensions to move in... So - the 2 dimensional image on the screen is the result of motion occurring in 3 dimensions.
 

Offline alancalverd

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And the third dimension is irrelevant except for a possible tiny asymmetry of the curve. Not that anyone would use an optical  Lissajous to make a precise sine/sine curve anyway. It's OK for arty photographs and stadium laser shows, though it's probably easier nowadays to wiggle the laser or LED directly, but it's a bit old-hat in either case and a lot more complicated to set up than a Spirograph.

The appearance of the figure does not depend on small movements of phasing. A stationary figure will have a fixed phase difference which can vary from 0 (to give a straight line) to 90 degrees (a circle). If the phase difference is a multiple of 90 degrees + a constant, ie  phase locked sine waves of different frequencies, you will get stationary multiple closed loops with a tilt. All that the z-induced phase error will do is induce a bit of jitter into your nice image.
 

Offline timey

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My interest doesn't stem from an arty point of view, nor musical...

What I am interested in is the wave period, ie: amplitude of vibration, of 1 sine wave being changed by the wave period, ie: amplitude of vibration, of the other sine wave, and that a 3rd wave period of vibration emerges as a result of this change.  It is the maths of these 3 dimensions of motions that interest me.  (Yes I can appreciate that jittering, or a Lissajous figure that is displaying movement is due to various degrees of 'out of phase'.

The Lissajous figure is a 2 dimensional representation of motion in 3 dimensions over time...  Are there maths that describe these motions?
 

Offline Colin2B

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The Lissajous figure is a 2 dimensional representation of motion in 3 dimensions over time...  Are there maths that describe these motions?
No, because as we've said before the lissajous figures are not a 2d representation of 3D.

What I am interested in is the wave period, ie: amplitude of vibration, of 1 sine wave being changed by the wave period, ie: amplitude of vibration, of the other sine wave, and that a 3rd wave period of vibration emerges as a result of this change.  It is the maths of these 3 dimensions of motions that interest me.
Just a point of terminology, wave period is not the amplitude of vibration.
What you describe doesn't happen in this tuning fork set up and doesn't need 3 dimensions. Have a look at Fourier transforms to understand mixing of waves.
 

Offline alancalverd

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Amplitude is the height of a maximum, or half the total span.

You can alter amplitude by adding waves of the same frequency. The Lissajous figure does not do this. The x and y amplitudes are the amplitudes of the original waves.

Period is the time or distance between two successive maxima.

You can alter periods by multiplying waves of different frequencies. The Lisassajous figure does not do this although the rate of repetition of a cyclic figure does depend on the frequency difference. The x and y frequencies are the frequencies of the original waves.
 

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