Speaker efficiency vs. power requirements

Your math is Ok, but 90 dB is not the starting point for your dynamic range. Dynamic range is the difference between the softest and the loudest, and 90 dB is pretty loud to start with. 120 dB is EXTREMELY LOUD, equivalent to a jet taking off. 140 dB is the threshold of pain. Your million watt amplifier producing 160 dB would destroy your hearing. A more reasonable 60 dB range would be 40 to 100 dB, well within the capabilities of most hi end amplifiers and speakers.

Your conclusion about amplifier requirements is not valid. Your dynamic range numbers for both analog and digital are off. Analog tape can have approximately a 60dB range. I've seen several different numbers regarding digital, but the effective range seems to be 80-85dB. The listening room also comes into play. A typical residential listening room has a background sound level of 50dB (if you live in a rural area far from trains, air routes and highways you could get down to the mid 30s). So if you set you system gain such that the softest sound level is equal to the listening room's background noise level, then you would need to produce a maximum sound pressure of 135dB to fully reproduce the digital medium's dynamic range. Assuming it could go that loud, which is a very big assumption, a 90dB sensitive speaker would require a mere 32-33,000 watts of amplifier power. With its smaller dynamic range, analog sources would only require 128 watts of amplifier power.

In the real world the above number are not particularly relevant. The measured dynamic range of recorded music rarely exceeds 40dB. Pop/rock music is typically in the 10-15dB range. Any intelligent listner rarely would listen at room sound levels above 105dB. A 90dB sensitive speaker only requires 32 watts of amplifier power to produce 105dB levels.

Yes, I think the flaw is starting with the 'efficiency' of 90db, and thinking of this as the base number for dynamic range.

So, a 90db speaker, with 100 watts will do 100 db, and 110 db with 1000 watts. Dynamic range will be from 0 (no current to speaker) to 100 or 110, respectively.

With the logic in the quote above, speaker efficiency is taken out of the equation, as it uses the speaker's efficency as the dynamic range 'floor.'

Your source is ok, I guess, its just said things in a kinda stupid way. This topic has been covered before. Every 10db increase is a doubling in SPL (sound pressure level, and I would call this loudness, colloqually (I know its spelled wrong)) and perceived loudness. 80db is twice as loud as 70db. 90db is 4x as loud as 70db (2x2=4). It takes ten times (10x) the power to double the SPL. So if you can play 90db with 1 watt, then 100db will take 10 watts,110db will need 100 watts, and 120db will need 1,000 watts. Got it. OK. So the first 4 sentences of your source are OK; its just said really weird.

He gets confused on the 5th sentence, or at least I am. If we need 60-70db dynamic range, well, to my knowledge, a bit limited, a 90db efficient speaker already has that dynamic range. It can play 90db with 1 watt so it can do 70db with even less power. What he's done is added the 60-70db onto the 90db to give a dynamic range of 150 to 160db. And from there it appears to be ok mathematically, yes you'll need 1,000,000 watts into a 90db efficient speaker if you expect it to play 150db loud. Thankfully, there are speakers w/ 100db efficiencies and higher, so we can make up for power with sensitivity/efficiency. And there's little reason to go beyond 120db because you'll start getting hearing damage. The 6th sentence is a no-brainer and his first five sentences are a little dumb, it he's just trying to support #6. Just disregard the last sentence (#7). As far as I know, loudness, i.e. how loud the system can play, is dynamic realism, the system can go from really really loud to quite. And the amount of power is in direct relation to how loud it plays once the system efficiency is taken into account. Hopefully, I'm not wrong on anything or I'll have confused you more trying to unlearn, relearn, unlearn, etc.

I may have screwed up in my previous post. But I don't want to think about it anymore. Try this.

Based on a 90db efficient speaker.

Desired SPL Needed Power
90db 1 watt
100db 10watt
110db 100watt
120db 1,000watt
130db 10,000watt
140db 100,000watt
150db 1,000,000watt
160db 10,000,000watt