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If there were 2 light beams what you are saying would be correct.

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?

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

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.

Yes he did...Quote from: Colin2B on 17/10/2016 09:30:45So 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?

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?

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:Quote from: timey on 17/10/2016 18:41:14My 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:Quote from: Colin2B on 17/10/2016 09:30:45So 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.Quote from: timey on 17/10/2016 18:41:14Thank 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.Quote from: timey on 17/10/2016 18:41:14I 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.Quote from: timey on 17/10/2016 18:41:14It 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.

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!

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?

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

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.

As to your statement that says that the mechanics creating the patterns are not occurring in 3 dimensions, either I'm just not understanding what you mean, or you need to think it through more thouroughly.

The mirror is attached to a tuning fork, the fork has a frequency it resonates at when hit, and when hit it rocks back and forth. This action tips the mirror from side to side, or up and down. These motions 'are' 3 dimensional, and it is these motions that cause the pattern, over time.

...and, I will most certainly have a look at the maths, but to be clear, are you saying that it is the Fourier transformations that are describing the 3 dimensional motions of distance change occurring between the mirrors?

If you are just interested in the Doppler shift from a moving mirror, why not say so? deltaf = 2v x f/c where v is the instantaneous velocity of the mirror.

So long as we can agree that Doppler shifts are occurring in the passage of the lights optical path?

What interests me is that the 'speed' of a Doppler shift can be translated into a period of time via the speed distance time formula where light is the travelling phenomenon, but enough of this for the moment...

Edit: To clarify, I am not referring to a frequency change in the light...

A Mossbauer effect of receiving a gamma ray conducted horizontally in a uniform gravity field will not respond differently if the gamma ray emitter is attached to a vibrating speaker cone. The photon will still be received.

No, it is not meaningless Alan... The speed that the mirror moves forward with is inherent with a distance.

The mirror only moves so far forward... Subtract the distance that it moves forward from the original distance, divide this distance by speed of light and you have a time value. The light didn't travel that distance, therefore the time it takes to complete the shorter distance is lesser. Subtract time value from the original time.A backward motion will do the opposite and add time to the distance.

Yes - the frequency of light changes in a gravitational gradient and this effect is thought to be due to Doppler shift, because distance between source and receiver is expanding or contracting. The frequency of the Doppler shift denotes the speed at which the expansion or contraction is occurring...

But we can see in the mechanics of the movement between the mirrors that the light does not travel the distance that is behind the moving forward mirror, nor the distance behind the moving back mirror, and neither of these forward or backward speeds can add or subtract from the velocity of the light.

Adding a vibration to the gamma ray emitter of the Mossbauer simply means the light has a little less time (forward motion), or a little more time (backward motion), in which to travel to the destination.

The Pound Rebka is a vertical experiment... Have you got any experimental data on a Mossbauer conducted on the 'horizontal' that states frequency change in the gamma ray via this vibration. I have never come across any myself...Provide me evidence of this and I'll be packing up my 'New Theory' on new theories as a waste of time!

You are correct in that you thought I had read and understood the Pound Rebka. I have, 'extensively' and do understand that the Doppler shift is thought to add or subtract energy for a 'longer' or 'shorter' wavelength.

the frequency of light changes in a gravitational gradient and this effect is thought to be due to Doppler shift, because distance between source and receiver is expanding or contracting.

If you have experimental data that describes the use of a speaker in a horizontal Mossbauer experiment that confirms the frequency change on the horizontal, then fair enough! As I said, my curiosity then over and done with.Do you? 'Cos as said last post, I haven't been able to find any...

Quote from: timey on 20/10/2016 18:28:32You are correct in that you thought I had read and understood the Pound Rebka. I have, 'extensively' and do understand that the Doppler shift is thought to add or subtract energy for a 'longer' or 'shorter' wavelength.You may think that, but it is not what you said. Alan is questioning:Quote from: timey on 20/10/2016 12:03:12the frequency of light changes in a gravitational gradient and this effect is thought to be due to Doppler shift, because distance between source and receiver is expanding or contracting. which is not true.

Thank you.

The frequency of light does change in a gravitational gradient. It is thought that the Doppler shift created by the velocity of the light source (star) moving away from point of observation (earth), ie: a distance expanding - or moving towards point of observation, ie: a distance contracting, changes the wave length of the light.Where have I gone wrong?

I am getting very tired of watching you insult the people that are trying to help you. You may find it amusing in your own passive aggressive way. I don't.