Eminent Technology ET-2 Tonearm Owners
Richard/Dover - Do either of you play flute? |
Dover. I don't think that personal attacks advance this thread, so lets both agree that we stick to our opinions on the subject or post relevant information. Shown here is a link to the Math on driven harmonic oscillators, a mathematical representation of an arm/ cartridge assembly. It shows in both formula and graphical terms what I have been trying to say. The Math is a bit of a struggle but fortunately the graphs show the results. http://en.wikipedia.org/wiki/Harmonic_oscillator#Driven_harmonic_oscillators We can see from the sinusoidal graph that the Transmissibility, for input frequencies that are say 25% or less of the resonant frequency, is 1. This means that there is total transmission of the input frequency into the structure. It moves as one. In other words the whole arm moves. At input frequencies above 25% up to resonance we get increasing gain and this area should be avoided. For input frequencies that are 300% of the resonant frequency we get transmissibility of around 15%, unless the structure is highly damped and we all agree, I think, that lots of damping doesn't sound good. So at 3x the resonant frequency we are loosing around 15% of the groove modulation, as the arm is still at this point moving back and forth sideways slightly. This is not a problem provided this 3 x resonant frequency is not a valid audio signal. Actually you would need to extend the graph out to around 6x resonant frequency before the transmissibility was approaching 0. Until we reach that point, part of the low frequency goove modulation goes into moving the cartridge and arm sideways and not into generating an output voltage. It was the discovery of this characteristic that led me to look into possible performance improvements in the LF area of the ET2. Since if the resonant frequency was say 6 hZ we would not have total transmission of LF modulation until we reached say 36 hz. Kuzma state that the horizontal resonant frequency for low to med compliance carts is in the range of 2.5 to 3.5 HZ, with an effective mass of 100gm. Resonant frequency is inversly proportional to the square root of the mass. So my arm at around 85gm would fall into the range of 2.7 to 3.8 HZ If we take the mid point for these resonant ranges 3 hz and 3.2 hz respectively, we are, in my opinion, in the Goldilocks range for the Kuzma and my arm. In that it is sufficiently high to avoid gain caused by eccentricity, since 0.75 Hz for a 45rpm record is less than 25% of the resonant frequency. But low enough to give virtually complete conversion of desirable groove modulation into output voltage. 19.2 hz (3.2 x 6) being at the lower end of what most systems can produce. If we look at the same numbers for a standard the ET2 we get a resonant frequency range of 5 to 7 hz for a 25 gm effective mass. This is comfortably above the 0.75 hz eccentricity problem, but if we take say 5 hz as the resonant frequency, we see that it will not be until we reach say 30hz before we have complete conversion into an output voltage. I dont think that this is desirable. Making the arm lighter still will extend this frequency upwards. http://en.wikipedia.org/wiki/Harmonic_oscillator#Driven_harmonic_oscillators |
Richard The resonance frequency figures we have from BT that we have discussed here. ET 2 (5 - 6 hz) ET 2.5 (2 - 3 hz) due to the larger spindle plus weighing a little more - not sure what the actual gram number is. So at 3x the resonant frequency we are loosing around 15% of the groove modulation, as the arm is still at this point moving back and forth sideways slightly. Based on what you are saying Richard - does this not then mean: ET 2.5 = 6 x 2.5 hz (midpoint for the ET 2.5) places it at 15 hz ET 2.0 = 6 x 5.5 (midpoint for the ET 2.0) = 33 hz The number 6 that you multiplied the resonance frequency by. Would this number need to change for a really high compliance versus really low compliance cartridge to be more accurate ? |
Chris. The 6 x multiplier is a factor extrapolated from the graph I posted the link to. 6 x being a figure where the resonant structure would likely be still, with some safety margin. It would not change with cartridge compliance. But the system resonant frequency could change outside the published figures if you were to use an outlier cartridge. A really stiff cart would push the resonant frequency up, moving further into the audio band. A really floppy cartridge would push the resonant frequency down, with a real risk of problems due to eccentricity. |
