Then to just complicate what I said above, the current output of an amp
comes into as well, to keep the said control over the speaker.
This is a common myth.
An amplifier can have a very low output impedance without having much 'current'. I put the word 'current' in quotes because Ohm's Law says without exception that the current flowing in the load is going to be directly related to the power being dissipated by the load, and that current will be the same regardless of the output impedance of the amp.
Example: 2 amps, one solid state with an output impedance of 0.1 ohm, and the other with an output impedance of 4 ohms are both making 50 watts into an 8 ohm speaker. How much current is present?
The Power formula is a derivation of Ohm's Law, and is current multiplied by voltage (1 watt = 1 Amp x 1 Volt). If you are dealing with an impedance, in this case 8 ohms, the derivation is Power = Amps(squared) x Resistance. So:
50 watts = 8Ohms x Amps squared. Solving for Amperage we get 2.5 Amps. Note that at no point does the output impedance of the amplifier figure into this- its not like an amp with a lower output impedance will somehow cause more current to flow. IOW the current is determined by the resistance of the load and how much power is being made.
Now there is the issue of the amp 'controlling' the speaker. The speaker cone moves in relationship to the energy applied to its voice coil and returns to rest when that power is taken away. What we are concerned about here is the issue of overshoot; that is to say any motion that is not having to do with the signal applied. This is where the concept of damping comes in. If the speaker is in motion and further is motion that is entirely overshoot then what happens is it will make a voltage, since there is a voice coil moving in relation to a magnetic field (this is known as 'back EMF'). That voltage has to be absorbed, and that is done by the output impedance of the amplifier, which acts as a short to that voltage.
From this you can see that the amount of current available in the amp really does not play a role in this damping effect. The output impedance however plays a huge role!
So what we can conclude is that a low current amplifier that can make the power needed will do the job as long as its output impedance is low enough to provide proper damping of the load.
FWIW, no speaker is known to need more than about 20:1 for optimal damping, and each speaker in a box (or not) has an optimal damping. For this reason back in the old days there were a number of amplifiers that had a variable damping control, which was a feedback control balancing current feedback and voltage feedback to allow the amp to have an adjustable output impedance over a wide range such that it could work with any speaker.
In the last 4 decades though there has been a race to get more and more damping factor out of amplifiers, but the effect has been to cause most loudspeakers to be over-damped. We've all heard 'tight' bass that has thump but not much in the way of definition. Its a thing that a lot of audiophiles like but its not natural- 'tight' bass does not seem to exist in real life. When the speaker is overdamped, the cone cannot make its full excursion before the waveform starts going the other way. So bass notes in particular get truncated- the body of the bass is less prominent although the thump is there. By limiting the damping factor to no more than 20 or 30 to one this effect can be reduced or eliminated with most modern loudspeakers.
