![]() ![]() 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. 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. 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. Fixed at both ends if we pluck the middle we get that characteristic shape of antinode in the middle and nodes at each end. Let's take the standard vibrating string in every school textbook. I may have assumed understanding of what vibrational modes involve, so perhaps we need to step back a bit. You're in the right direction but veering off to left field. 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? A frequency that is related to the plates own energy of e=mc^2. 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. 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. 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. In the second video it is shown that frequencies are being driven to the plate directly. The bowing has to be just so, or a tone/node pattern cannot be achieved. Note that some of the bowing ie: added energy/frequency does not cause node patterning. 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.īut 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. 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? 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? The Lissijous patterns are being created by the extremities of the vibration of the mirror. ![]() The second answer in relation to the first is interesting in relation to SR comments and time perturbations.Īs you pointed out, node patterns are created in the areas of least vibration in the plate. "Significantly, the combined wave function of the system and environment continue to obey theSchrödinger equation." Please note the use of the timing function.*Ĭorrect 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? To get further understanding I watched the above. 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". If the Hydrogen spectrum had energy levels related to 1/n, this may even be compatible with the Pythagorean ideal of harmony. ![]() You may try (with great difficulty) to construct an instrument that has similar resonances to the Hydrogen spectrum. By exciting the atom with difference frequencies of light, you could graph the spectral response of resonances to the incoming light. Schrödinger's equation describes the electron energy levels of an atom. By graphing this in two dimensions, you could reconstruct the Chladni pattern. ![]() By varying the frequency of the incoming sound, you could graph the spectral response of resonances to the incoming sound.ĭoppler shift of a laser beam can be used to measure the frequency of vibration of the object from which it is reflected. 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. ![]()
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