How big do PA speakers have to be?
Another question is, "How loud does a PA system have to be?" The answers from many people would be, "Very big" and, "As loud as possible".
This accounts for much of the dreadful sound to be heard from PA systems, other than those operated by people who really understand sound and sound engineering of course.
Here is one example: The classical guitar. This is a nylon-strung, purely acoustic instrument. It isn't very loud and is only really capable of satisfying audiences of up to 200. If the auditorium is any bigger than that, the sound will be uncomfortably quiet.
The solution is to use a small-diaphragm capacitor microphone,preamplifier and amplifier of course, and one small hifi speaker - a good one.
Why a small-diaphragm capacitor mic? Because it will give the most accurate sound when carefully positioned. If it has an omnidirectional pickup pattern, then so much the better.
Why one speaker? Because the guitar itself is a point source - why would it need to be spread out across the width of the stage? The speaker should be placed close to the instrument, but bear in mind that the closer it is, the greater the risk of feedback (howl round). There has to be a compromise here.
With a system such as this you can double the sound pressure level (+6 dB), and the amplification will be undetectable. Quadruple it (+12 dB) and it should still sound very natural. But the higher you go beyond that, the more obvious it will be that the sound is being amplified.
For the very best sound, use an electrostatic loudspeaker. That is the only type of loudspeaker that doesn't actually sound like a speaker.