Cartridge Loading and Compliance Laws

Dear Jeremy72: Laws?, IMHO there are no laws about but only theory about: that sometimes works and sometimes does not it depends on cartridge overall characteristics and tonearm it self.

IMHO it is not easy to take as a rule/laws a " generalization " like the resonance frequency range: 8hz to 12 hz. In this subject I think we can do better if we know what in specific we/you are talking about: which cartridge and which tonearm as which problems you are experienced with or what you don't like or want to improve at quality performance level.

I think that if you bring here that information some of us could help you with out be speculating on something we really can't even imagine.

regards and enjoy the music,
Raul.

So from what you guys are saying if an arm had an eff. mass of say 14g then if you somehow made the counterweight heavier then you would automatically be reducing that number? Not sure I understand... if you have an arm that is 14g eff. mass, then how is that number able to be changed by increasing the weight on the end? Isn't it is what it is by design? Maybe you are just kind of manipulating things is what you are saying, to increase the res. freq. of the two.

So many times have I read about the 8-12Hz cart/arm res freq guideline its just like it seems to be a law to me because these numbers are the ones always brought up. Now people some times claim 9 or 10 is soem magic number even. I am no analog wiz or do I understand all of this stuff I am just wanting to understand what the hecks going on so I don't wind up putting together something that does not go together and sounds awful or has some weirdproblem.

"Some arms have multiple weight systems, so if you can use a heavier counterbalance weight closer to the arm bearings that will get you lower effective mass as opposed to lighter weights further out."

What is the theory behind this? The heavier counterweight increases the effective arm mass. Also having the counterweight closer to the bearing gives a more stable tracking. This is what I did with my 11g tone arm and now the low compliance Koetsu grooves fine.

When we talk about tonearm effective mass, we are really talking about inertia. And when we talk about cartridge compliance, we are really talking about spring rate. Not to sound confusing, but high compliance is low spring rate and low compliance is high spring rate. So the resonance frequency of the tonearm/cartridge system is simply the square root of the cartridge’s spring rate over the sum of the masses. It is the classic spring/mass equation. The system will become very excited at its resonance or natural frequency meaning it will mistrack or even skip.
The moment of inertia of the tonearm about its pivot is I=mr2. So moving the counterweight further from the pivot point increases the inertia (effective mass) by the square of the distance whereas keeping the counterweight at the same distance and increasing the mass is a one to one change in inertia. That’s why using a heavier counterweight closer to the pivot reduces the tonearm effective mass.
The tonearm is on a pivot bearing with as little friction as possible, so it is important to have a tuned system that does not get excited by vibrations from the record/platter or vibrations external to the turntable. The stylus is connected to a suspension which gives it its spring rate. As the stylus moves up/down and left/right on the record it is pushing against the tonearm. As long as those motions or vibrations are not near the tonearm’s resonance point, the tonearm remains stable.
When you pluck a spring, it resonates at its natural frequency. A string nearby tuned to the same frequency will vibrate on its own because it is excited by the other string’s vibrations. That is called sympathetic vibration. The same holds true for the tonearm/cartridge system. The 10Hz +/-2Hz natural frequency is a rule because it works. Music ranges from 20Hz- 20kHz. So if the tonearm/cartridge system is tuned too closely to 20Hz, then the arm could become excited when playing music on the record that is close to 20 Hz. 10Hz being half of 20 keeps the tonearm/cartridge system safely away from the range of the music. Now at the other extreme, footfalls and other low frequency sources in the 5-6 Hz range will excite the tonearm if it is tuned too low. So again, 10Hz being double of 5 helps reduce the tonearm’s sensitivity to footfalls and such.
I hope this all makes sense.