The benchmark was 100kHz. And the amplitudes are probably decreasing asymptotically. Anyway if you find anything better please feel free to share. As I already stated I am as much in the dark with this one as everyone else here who is not a mechanical engineer.
Yes, well, that shows what can happen when idealized mathematical models break down in systems more complex than the assumptions of the model. Without any attempt to be complete (or completely accurate!), damping of vibration modes due to friction in the metal would probably attenuate higher order modes pretty fast. Maybe faster than one cycle. Also, the tuning fork would probably have to be excited with a forcing function with high enough frequency components in to let the tuning fork ring at some really high frequency mode. High velocity rifle round might an interesting experiment. Then again, some modes would require a propagation velocity faster than the speed of sound in the metal (consider the time allowed for one cycle and some need for mechanical displacement during that time, with sufficent displacement needed to bump along the next adjacent molecule in the time period), and eventually, faster than the speed of light (maybe), and so on. In other words, the mathematical model is for an idealized tuning fork, not a real one.
For a small tuning fork, 100kHz might be within reason. Here again, probably not ever going to make it to someones power amplifier without a lot of special effort. Obviously, besides tuning forks, quartz crystals can mechanically resonate at many MHz, but we wouldn't feed it into our power amp.
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I have a 1/8 inch bruel and kjaer condenser mic that we used to use at zenith radio to test ultrasonic remote controls. Was flat way past 50khz.
Back in the days where your vacuum cleaner would turn the tv on and off 😀
Back in the days where your vacuum cleaner would turn the tv on and off 😀
Mark - glad you mentioned that in order to start vibrating, the fork needs to be excited somehow. And that discontinuity moment - from non vibration to vibration - is responsible for the Gabor thing.
But let's look farther in the chain. Even with the filtering produced by the mic / preamp / etc, the amp will also have at its input a moment of discontinuity (no signal -> signal) and this Gabor thing strikes again.
Unless we find some contrived explanation on the lines that the fork never actually stops producing sound, or that the noise is part of the signal and it contributes to it in such way that the spectrum becomes BW limited.
But let's look farther in the chain. Even with the filtering produced by the mic / preamp / etc, the amp will also have at its input a moment of discontinuity (no signal -> signal) and this Gabor thing strikes again.
Unless we find some contrived explanation on the lines that the fork never actually stops producing sound, or that the noise is part of the signal and it contributes to it in such way that the spectrum becomes BW limited.
I will disagree. The impulse of even a high speed rifle round is nowhere near the infinite speed of a mathematical simplified model of it. And in reality, there is no perfect square wave, only an imaginary mathematical concept in Gabor's head. A useful concept, but one to be used with an understanding of what it is.
The fork will absolutely stop working at some practical frequency limit. Again, the model you found assumes the tuning fork is made out of a solid piece of lossless elastic material. It is not in fact solid, it is made of atoms, and as a metal may have some crystalline structure, but in no case as tightly packed as quartz. It is also not in fact lossless, it has friction. If you keep bending it, it will heat up. Therefore you have found a model that doesn't work for all the cases you are interested in. Don't feel bad though, lots of scientists and engineers have had similar mishaps. Look at the variables in the equation they offer, Youngs modulus is for elasticity, they also include density. I don't see any variables to account for friction, or speed of sound in the material. By the way, friction in a mechanical vibrator is as resistance is to an LC tuned circuit. It damps the oscillation and reduces Q.
Beyond that, the model assumes the traverse vibration mode can stably exist at very short wavelengths compared to the other dimensions of the tuning fork, such as the width of the tines. They do mention it gets more complicated around the bend in the tuning fork, but they leave it at that. They also, I presume, assume that a mechanical engineer will be familiar with the limitations of the model.
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We're dangerously reaching the point where some smarthat will wield the "Fourier denier" or "Gabor denier" labels.
Let the joke be with them, as we're starting to touch the subject of continuum vs discontinuum in physics. And that's where more interesting labels can be returned.
"I consider it entirely possible that physics cannot be based upon the field concept, that is on continuous structures. Then nothing will remain of my whole castle in the air, including the theory of gravitation, but also nothing of the rest of contemporary physics." (confession of Albert Einstein near his life end)
Let the joke be with them, as we're starting to touch the subject of continuum vs discontinuum in physics. And that's where more interesting labels can be returned.
"I consider it entirely possible that physics cannot be based upon the field concept, that is on continuous structures. Then nothing will remain of my whole castle in the air, including the theory of gravitation, but also nothing of the rest of contemporary physics." (confession of Albert Einstein near his life end)
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Right. Gerard t'Hooft is still alive, and is a theoretical physicist with a Nobel prize. He shares some of Einstein's sense about determinism verses randomness, and the reality at this point it we don't know where it all ends. What we do have now, however, that does work, are finer and finer grain models depending on how deep down we need to go. Not deep enough for everything, but deep enough, I think, for the problem at hand. Trust me, I ask you, the model you have is rather too limited in frequency range for the point you would like to draw out. I'll let you in on a little secret. Don't tell, okay? I'm not a mechanical engineer, nor an electrical engineer, nor a psychologist. I'm not anything. No kidding. About the equivalent of a PhD though I was told by a science department chair at Stanford where I spent 20 years as an engineer among other things, and that was long after being a faculty member at UCLA medical school, but no paper hanging in the wall to show for it. There you go. I kid you not. Anyway, that's the truth, and I told you the truth as I know it about the tuning fork. I think we should leave it here.
I know. I just pushed the defence to the last possible grasp. Beyond that we're definitely getting into particle physics, where many of the macro based theories start to show their limits. I do respect your argument too as well written and logically coherent.
I don't know if this can contribute to the science of wave form analysis applied to music but we can draw arbitrary wave forms and reproduce them through amplifiers and see exactly how the opamp can carry the arbitrary wave form by comparing the image to the model.
I will report as soon as finish my stereo microphone with optical capsules. I will need a guidance how to test them with a spark gap, otherwise there is no transducer that can be used practically. Can you help me Scott?
I have two B&K capsules that work to 100 KHz. Scott shared the spark gap info and it looks like its not real strong on ultrasonics actually. I have been looking at Piezo's for some ultrasonic source but not sure what to go for. They all seem to have a strong resonance and limited bandwidth.
I have a Pioneer Ribbon that does seem to make it to 70 KHz if the mike is in exactly the right place. Otherwise more like 35 KHz. Even so I have 1/4 ECM mikes that follow it quite well to 35 KHz. http://www.diyaudio.com/forums/equi...e-mic-speaker-measurements-5.html#post4898890
I have a Pioneer Ribbon that does seem to make it to 70 KHz if the mike is in exactly the right place. Otherwise more like 35 KHz. Even so I have 1/4 ECM mikes that follow it quite well to 35 KHz. http://www.diyaudio.com/forums/equi...e-mic-speaker-measurements-5.html#post4898890
Train wrecks, meteor impacts and nuclear explosions. I want those faithfully reproduced in my living room.
I don't know about speakers for that, but a little next generation bioengineering, a few electrodes, and a black box stimulus generator, might be able to give you the VR equivalent. Some of the pre-existing wetware may be just waiting for it: https://en.wikipedia.org/wiki/Exploding_head_syndrome
I am not an expert on these matters, but I would expect that the simple model breaks down when the wavelength of oscillation (along the tine) approaches the thickness of the tine (across the tine). Apart from this, I would assume that the metal becomes acoustically lossy at higher frequencies. To get high frequency mechanical oscillation in objects of 'normal' size you need very stiff very low loss materials such as quartz.scott wurcer said:
As they were writing for physicists they probably thought they didn't need to say this. They might be surprised to hear that the fact they did not specify a limit on n is taken by someone as proof that n is unlimited. When you write something sensible it is virtually impossible to plug all the potential holes through which someone somewhere will attempt to extract nonsense from it; you have to assume sensible readers.
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