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=lRFysSAxWxIHere 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=wvJAgrUBF4wHere 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_b4Correct me if I'm wrong but these laser patterns must be caused by Doppler shift right?

https://m.youtube.com/watch?v=t6nGiBzGLD8To 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_collapseQuote:

"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-effectThe 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?