[Radio Wrangler]

The moving coil loudspeaker is both a motor and a generator. If you apply a fixed voltage to it, current will flow, applying force to the moving mass which will accelerate. As the coil gains velocity, in moving through the magnetic field, it will generate voltage opposing the current (Lenz' law and Faraday) eventually the coil will reach speed where the 'back EMF' opposes the applied voltage and decreases the current. The force decreases and the cone velocity is at a limit set by the applied voltage.

At constant voltage, the cone wants to move at a constant (and proportional) velocity.

A cone moving at constant velocity tries to shift a constant volume of air per second

A constant flow rate (litres/second) acts as a constant pressure.

So a loudspeaker tries to be a voltage-to-pressure transducer. Our ears are essentially pressure sensitive, so this all seems to fit.

This is why we try to drive speakers from controlled-voltage sources, and why we don't get too upset by speaker impedances wandering around rather a lot.

We want the voltage supplied to the speaker to be rather stiff... to not vary much if the current taken changes. This has a nice side effect of trying to damp and control any resonances in the speaker as well. So the ratio of speaker impedance to amplifier impedance is called 'Damping Factor' It isn't the be-all and end-all, but you want a reasonable amount.

Um, just a minute... the bigger the damping factor, the bigger the difference in the speaker input Z and the amplifier output Z..... so the match is worse!

Right! Who said they needed to be matched? We have a situation of what we want is an efficient, unidirectional flow of power. AND the distance is trivially small at the frequencies concerned. An Amplifier output impedance of damn all is perfectly fine, and an 8 Ohm speaker is OK.

Zero Ohm transmission line is tending towards infinite diameter conductors spaced zero mm apart. So the cable shamen chose to match the speaker's nominal value and ignore the amplifier Z. Actually this is OK if we really had a match at the speaker end. But speaker impedance bounces all over the shop, and at the hundreds of kHz and above region where the oscillations start up, then all bets are off. So the matched at either end business is a big joke. Just thank your chosen deity that the cable is far shorter than a wavelength, and so it doesn't really matter at all. Except to people with infinite aural capability.

When cables are long compared to a wavelength, say a radio transmitter to an antenna. It is usual to match the cable to the antenna (minimising any reflection when the signal reaches that end of the line, and to not care about matching the transmitter to the line - it doesn't matter if there is no backwards flow of power to be reflected.)

Many people Think the transmitter and line are matched, but they aren't. A transmitter is designed to feed say a 50 Ohm line, but that doesn't mean it looks like a 50 Ohm source. It just means that the voltages and currents in a transmitter working into that load are comfortable, and nothing is about to burn up. The transmitter suits a 50 Ohm load (and vice versa) but this isn't the same as matching in the mathematical sense.

David