Speaker efficiency vs. power requirements

Recently someone gave me the "math" behind speaker efficiency ratings and power requirements. Although I am not sure if the information below is 100% accurate, it is what I have been told. Can we lay this on the table for discussion and try to resolve this confusing issue once and for all?

0 db is a power ratio of 1. Records and tape have dynamic ranges of 30-40db. To achieve a 30db dynamic range requires a power ratio of 1,000:1 and 40 db requires 10,000:1. So if you assign 1 watt of power to a speaker yielding 90db SPL, you need 1000 watts to deliver a true 30db dynamic range. With digital material we find dynamic ranges of 60-70db requiring power ratios of 1,000,000:1 & 10,000,000:1 respectively. Power amps of 1-10 million watts are not feasible today but the point is, more power offers more dynamic realism. Forget power vs. loudness because that really is not a factor in the overall scheme.
Power ratio??? Never heard of it. What is it?
It appears the flaw in your reasoning is that speakers rated at 90dB can and often do play at much lower levels. By definition a person can hear any level of signal above the noise floor. Consequently think of starting at the whole system's noise floor - including the noise embedded in the software - not the efficiency rating of the speakers to discern your dynamic range. Also remember that the power ratings of amplifiers do not dictate output. The wattage ratings serve as one measure of an amp's prolonged sustainable capability without failure.
I DON'T KNOW WHO YOU WERE TALKING TO BUT BOY ARE THEY CONFUSED. Speaker sensitivity is simply the amount of db's produced as a reference (usually 1 watt at 1 meter). What your amp kicks out are electrical watts (you know the RMS variety) while what's (sorry for the pun) coming out of your speaker are acoustic watts. Even a very powerful 200 watt amp may in fact only have a watt or two coming from a speaker, after the inevitable heat loss from electrical to mechanical. The wattage of your amp must be taken in context with your speaker sensitivity, how far you listen from, what kind of music and how loud? You are also confusing dynamic range with the decibel scale. The decibel scale is a fixed number, 70 db is always 70 db. Dynamic range is just the ratio of a quietest sound to a loudest sound (also called signal to noise ratio). Don't forget that power ratings double with a corresponding 3 db change. Therefore a 200 watt amp has twice the wattage of a 100 watt amp and is only 3 db louder, which is about the limits that you can detect by ear. I have thrown out some basic stuff out there as I am mainly a biology major. I'm sure some physics major or enginneer can add plenty more.
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
And that would give you a dynamic range of 160db, and it'll probably kill you along the way!
Hello great information and thanks for the input - just to clarify - the information I posted at the top is NOT my conclusion. This is however what *I* was told by someone who claims to know this stuff. As I pondered the statement, I grew unsatisfied with the logic and chose to post for discussion.

To clear some things up for some of you:
The mention of 90db is in regard to the speaker efficiency. I believe this number was selected since it was the rating of my speakers.

Another couple questions to further enhance this discussion:

1) Given the rated efficiency of a speaker - how does the Ohms rating effect power requirements? For example, a 90db speaker at 6Ohms.

2) Depending on which speaker, isn't it true that different frequency requirements may have more or less efficiency at varying ohms? What does this do to the overall power requirements?

And to top it off, what about impedance?
Just to further complicate the issue... a 3 db increase doubles the power (wattage). To double VOLTAGE, it takes a 6 db increase.
Drjjpdc: Your comment "Therefore a 200 watt amp has twice the wattage of a 100 watt amp and is only 3 db louder, which is about the limits that you can detect by ear." is WAY off base. I use a dB meter on a daily basis at work and differences of less than 1 dB are easily discernable on my less than "hi resolution" test bench using a 4" communications grade speaker and test tones. Some people have demonstrated hearing differences down into the millibel range under test conditions.

Herman: 100 dB's is too quiet. I would say that a system should be able to do at least 110 dB's at the seated listening position. This is not too hard to accomplish so long as you have enough amplifier for the size room that you are in and relatively efficient speakers that don't go into massive compression when fed some juice. Obviously, using more efficient speakers in a smaller room would put most people WAY ahead of the game. Sean
Sorry Sean I did not mean to say that nobody can hear less than 3db differences. I meant to say that in the context of our discussion on amplifiers, a 3db difference and doubling amp power is barely discernible as hearing a loudness difference in the 2 amps. That is different than perceiving loudness changes in sound during decibel testing. That is why in audio circles if we have a 100 watt amp, we need to buy at least a 200 watt one to hear a noticeable difference in power as opposed to hearing subtle differences.
I was just reading Robert Harley's chapter on amplifiers in his book, "The Complete Guide to High-End Audio," last night. He explains all this fairly clearly. He makes it pretty easy to understand and calculate an amps potential versus speaker requirements, how to determine the dBW power rating, what it means, and why it is useful. Give it a read. You'll get all you need.