Speaker sensitivity, impedance, and calculating amp power

OP:

If you are interested in theory alone, start with understanding power and sensitivity (not efficiency) at 1 meter.

Assume the amplifier is a perfect voltage source, and the speaker an ideal 8 ohms. Then understand that you can use the power in dB to tell you the difference in speaker output.

dB louder = 10 log (power / 1 watt)

So, if you h ave an 89 dB sensitive speaker, and apply 100 watts, the output at 1 meter will be 109 dB.

The truth is that an ideal speaker with flat frequency response speaker has equal voltage sensitivity at all frequencies, but the power consumed at any frequency is proportional to the inverse of the impedance, so the idea of using power to determine output is a cheat. We’re really using the amps equivalent voltage difference.

So long as your speaker is exactly 8 Ohms, then we can use the power calculation (above) interchangeably with the voltage calculation, below:

db louder = 20 log ( voltage / 2.83V)

The real problem we have is that amps are not sold by voltage output, but by power, but in fact, power amps are not power amps at all, they are voltage amps with (ideally) zero output impedance. That is, a power amplifier does not multiply the input power. It multiplies the input voltage and produces whatever current, and therefore power, is needed.

I’m overfilling your bucket here because I want you to reconsider your question. :)

This handy Wikipedia entry may further confuse you:  https://en.wikipedia.org/wiki/Decibel


Best,

E

Avoid any speaker that dips below 4 ohms through the bass section.Above 5-6 ohms is even better.The flatter the impedance curve the better.

For every 3db increase in SPL the amplifier power required doubles. 1 watt, 2 watts, 4 watts, 8 watts, 16 watts, 32 watts, 64 watts, 128 watts ... And a 10db increase in SPL (double the loudness) requires about 10X the power.

SPL isn't the only consideration when choosing an amp. Factors such as headroom for transient spikes and damping factor play key roles. I had an amp from a specific manufacturer that was rated at 200w into 4 ohms. I had a sense (how's that for a scientific analysis) that it just didn't seem to have enough power to control my speakers which are rated at 96db. I sold it and went for the same brand with an output of 370w into 4 ohms. My system improved because the sound was tighter and more detailed than previously. I wasn't listening any louder, that wasn't my goal. The larger amp was able to control my speakers much better and give me more detailed and cleaner performance. Again, power is not only about SPL.

I'll go buy the Harley book. I'll try to consult it before asking questions like this. I assumed there were no prereq's for asking a question.
@millercarbon — I'm interested in both. It starts with a practical question but leads into theoretical ones, which I want to get a handle on. I'm not seeking to ask questions with hidden motives. No need to out me.
@erik I'll reconsider my question. 

Another way to have asked the question would have been:

"What role does impedance have, if any, alongside other factors in the calculation of how much power should be used to drive a speaker comfortably?"

@tomic601 How loud? SPL of about 80 db, which I would assume with classical/jazz would have peaks of about 100 SPL?

I have been using various calculators to try to see how all the factors I mentioned in the OP vary. For example, there's this one from Crown: www.crownaudio.com/en-US/tools/calculators#amp_power_required
And a nice sheet linked to here on the Hans Beekhuyzen Channel www.youtube.com/watch?v=itKqSWH07_Y

The reason I asked the question was because the calculators I found do not mention the impedance of the speakers. Again, I'll reconsider my question based on what Erik said and what the Harley book says. If I could delete the question, I would.