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Everything posted by JohnCockburn

  1. Thank you David. You really are too kind. To be honest I don't know what came over me. Some kind of weird episode of craziness.
  2. Don't worry. I'm sure I'll quite rightfully face some consequences.
  3. David. I owe you a humble apology. Looking back over the way this thread developed, I can see that at one point i got hold of the wrong end of the stick about what you were saying, and ended up talking nonsense. What you were saying was right. I was wrong. And I also realise that there is a way that Tartini tones arising from beats could appear in a Fourier transform. If the difference frequency periodicity excites another resonance, such as an open string. That would do it, I think. Cheers john
  4. Honestly, David. Go away and read a high school physics text book.
  5. I edited that comment so as not to appear rude. But I see you managed to grab it. I have enormous respect for you as a violin maker.
  6. No, a flat line has "zero amplitude". Doesn't matter where on the screen it is. That's just a DC-offset. Of course, amplitude without frequency is meaningless, because nothing is oscillating.
  7. Right. We really are in the "post truth" world now.
  8. David. This is just foolish. No-one was talking about a waveform without amplitude. But a waveform of constant amplitude. This really is weapons grade nonsense.
  9. Always fancied having a go at Buddhism. Might help make me a bit less lairy.
  10. Sound ...of.....man...banging...his.....head....against....brick .......wall...........
  11. Anyway, to get back to the discussion of “Are Tartini Tones just high frequency beats?" If we want to demonstrate the phenomenon of beats, we take a signal that’s a linear superposition of 2 sinusoidal waveforms of frequencies f1 and f2. ie: S = sin (2πf­1t) + sin (2πf­2t) We arrange things so that we can vary f1 and f2. When these frequencies get within a few Hz of each other, we can clearly hear “beats” ie periodic increases and decreases in the loudness of the signal, at a frequency of f2-f1. The important thing to realize is that these beats aren’t in any sense an “additional signal”. Its just that when we add waveforms together, we will encounter situations when they will interfere constructively and destructively. Sometimes they’ll boost each other, sometimes they’ll partially cancel out. This is what gives the beats. Periodic phase cancellation. So whether we can hear beats or not, the signal is always: S = sin (2πf­1t) + sin (2πf­2t) NOT S = sin (2πf­1t) + sin (2πf­2t) + woowoo Because the woowoo is already in the addition of the sine terms. Fourier transforming this signal is trivial. just delta functions (spikes) at the frequencies f1 and f2. So that’s all we see in the FFT. Nothing, ever, at the difference frequency f2-f1. CTstanzio’s frequency spectrum, and ones I’ve taken myself, many times, clearly shows the Tartini tone, as well as the sum and frequency doubled signals predicted by theory. If the Tartini tone can be seen in the FFT, it can’t have its origin in beats. No way. So, how can we generate a difference frequency signal, that will show on an FFT, from 2 waveforms of frequency f1 and f2? We have to arrange it so that we multiply the waveforms together, rather than adding them. For waveforms on paper, we can of course, just calculate the product and display the results on our computer screen. To do it for physical waveforms we have to find a physical way to multiply or “mix” the waveforms together. This is done by passing the waves through a nonlinear system. (see the attached appendix file- I'm not going to spend ages typing out all those trig functions here ) One of the terms produced in the nonlinear mixing of our S = sin (2πf­1t) + sin (2πf­2t) signal is a multiplicative one. You’ll need to look at the attached file to see exactly how that arises. The upshot is, that after application of trig identities, we can write the multiplicative term as: 2Cos (2πf­1t)* Cos (2πf­2t) = Cos (2π(f­1+f2)t) + Cos (2π(f­1-f2)t) (i've changed from sin's to cos's for consistency with the appendix. As I'm sure you know, this doesn't matter. A cos is a sin with a 90 degree phase shift) The second term on the RHS is the tartini tone, the other the sum frequency tone. Fourier transforming this gives you peaks at the sum and difference frequencies in the FFT spectrum. So hopefully, we can see how nonlinearity leads to the tartini tone. This nonlinearity can be in the auditory system, the instrument , the microphone/electronice you use to record the signal, etc etc. So there you go. JC JC_TARTINI_APPENDIX.pdf
  12. Doesn't matter. Apart from "displacement from equilibrium" which in general, isn't the definition of amplitude. Amplitude is the maximum displacement from equilibrium. So constant amplitude, ie with no modulation or fluctuation of the amplitude, for a sound wave, for example, means that the sound has constant intensity, or perceived loudness, if you will. Changing the amplitude changes the loudness. "Amplitude without modulation produces no sensation of sound, only something ranging between a weird feeling, and pain" No. Wrong.
  13. "Amplitude" doesn't mean what you seem to think it means.
  14. Nice spectrum in this thread. Unambiguous proof that Tartini tones aren't high frequency beats.
  15. Change of plan. I'll answer the points here. David Beard: I didn’t mention individual molecules. Each individual molecule in the air is undergoing translational motion in random directions, with a spread of velocities given by the Maxwell-Boltzmann distribution. The root mean square speed of a nitrogen molecule at room temperature is about 500 m/s. What’s relevant for a sound wave isn’t this individual motion. It’s the collective displacement of all the molecules in an arbitrary “slice” of gas in the direction of propagation that’s important. The molecules are, of course all still undergoing random motion, but they all have collective oscillatory motion in the direction of the pressure wave propagation. It's a bit like the drift velocity in the direction of the current experienced by the randomly-moving conduction electrons in a metal. I don’t get what you mean by “only the collective pressure has the frequency” The acoustic pressure and the displacement oscillations are fundamentally linked. Displacement oscillations lead to local particle density fluctuations, which lead to local acoustic pressure fluctuations, as they must from the ideal gas equation of state. And all vice-versa of course, if you prefer.
  16. This isn't what Shunyata intended for his thread, so I'll start a new one. Probably tomorrow.
  17. Wow. This is quite an impressive display of attempted collective bullying. As I'm being attacked on several fronts here, it'll take me a little time to respond. Don't take this as a sign of weakness
  18. No, because beats arise through simple linear superposition of the component waves. There's no signal power at the beat frequency, just an amplitude fluctuation. That's why it wouldn't be seen in an FFT. There are no air molecules oscillating back and forth at the beat frequency Tartini tones require mixing of the 2 source wavelengths via a non linear medium. This leads to a difference signal that does have signal power, can move air molecules and can be seen in an FFT. The idea of Tartini tones being high frequency beats is wrong.
  19. Not at all. Have you actually read my earlier posts in the thread?
  20. Christ almighty. Yes of course, that's what we were talking about before you entered the realms of science fiction with your amplitude modulation nonsense.
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