Just how much more power is "twice as loud"?

[okcrum]

After asking this question several times here on TB and getting no satisfactory answer, I decided to try to answer it myself. I keep reading here that it takes 10 times the power to sound twice as loud. I believe that's incorrect, and I will attempt to explain why.

Traditionally, in engineering, 3 db power, 6 dB voltage, 3 dB SIL, and 6 dB SPL are all considered to be "twice as loud". This equality only holds if, for example, the loudspeakers used are not bottoming out, amp is not clipping, etc. for the sake of this post. I know there are other effects, but I am trying to keep it simple and stay on topic.

3 dB power = twice the power
6 dB voltage = twice the voltage
3 dB SIL = twice the Sound Intensity Level (acoustic power through a given area - think of a sound window)
6 dB SPL = twice the Sound Pressure Level (intensity of the acoustic field, relevant to how our ears perceive sound - at a single point)

The numbers are different for the same thing because the formulas for dB are different for different units of measurement. They all relate to the same sense of "twice as loud".

So twice the power is twice as loud, right?

Well, yes, from an engineering standpoint. But that's not all.

Enter psychoacoustics (the science of sound perception) - bolds are mine:

"The sone is a unit of perceived loudness after a proposal of Stanley Smith Stevens (1906-1973) in 1936. In acoustics, loudness is a subjective measure of the sound pressure. One sone is equivalent to 40 phons, which is defined as the loudness of a 1 kHz tone at 40 dBSPL. The number of sones to a phon was chosen so that a doubling of the number of sones sounds to the human ear like a doubling of the loudness, which also corresponds to increasing the sound pressure level by 10 dB, or increasing the sound pressure by a factor 3.16 (= √10). At frequencies other than 1 kHz, the measurement in sones must be calibrated according to the frequency response of human hearing, which is of course a subjective process.

The study of apparent loudness is included in the topic of psycho acoustics. Volume in acoustics is used as a synonym for loudness. It is a common term for the amplitude or the level of sound."

What this is saying, simply, is that perceived loudness of sound doubles for every 10 dB of SPL. And here's where I think the old wives' tale comes from: "To sound twice as loud, you need ten times the power."

Ten times the power is 10 dB more power, which is not 10 dB more SPL. It's 20 dB SPL, because the formulas are different.

The correct power increase is in the psychoacoustic quote above, and here's where it comes from: "increasing the sound pressure by a factor 3.16 (= √10)".

3.16 times the power = 5 dB more power = 10 dB more SPL.

THIS IS HOW MUCH MORE POWER IT TAKES TO "SOUND" TWICE AS LOUD. About 3 times the power, in short.

So here's what I think:

1) Lazy reading of the psychoacoustic theory started the 10x power "old wives' tale".
2) In purely engineering terms, twice as loud is twice the power, which is 3 dB power.
3) In perceived (psychoacoustic) terms, twice as loud is 3.16 times the power, which is 5 dB power and 10 dB SPL.

Note that the loudness curve does not enter into this discussion, because all it does is raise or lower the floor for ear sensitivity. It doesn't change what power increase we hear as "twice as loud", only the absolute power needed.

I've stayed away from describing the differences between power fluxes, fields, gradients, etc. to keep this post a bit more accessible and short.

Thoughts?

[Selta]

A Ph.D wrote this, so I trust it to be fairly accurate:

http://trace.wisc.edu/docs/2004-About-dB/

Also, you have to realize that 3.16 is only at 1kHz, not across the spectrum. Different frequencies take different amounts of power to be perceived as 2x as loud.

[billfitzmaurice]

Originally Posted by okcrum

And here's where I think the old wives' tale comes from: "To sound twice as loud, you need ten times the power."

Those 'old wives' were the audio engineers who invented the decibel scale. The 10dB differential that on average is required to sound twice as/half as loud isn't something that was decided on lightly.

Ten times the power is 10 dB more power, which is not 10 dB more SPL.

Yes, it is. This also came about by design. It is imperfect, as it assumes a speaker that remains linear, and none do, but all that means is that once speaker thermal and mechanical power compression sets in it takes even more than 10dB more power to get 10dB more SPL.

5 dB more power = 10 dB more SPL

Incorrect. See above.

[Jim Carr]

I think most of us say 1000 watts is twice is much power as 100, not that it is twice as loud, though no doubt we goof at times. So? Close enough for horseshoes, hand grenades, and bass rigs, IMHO.

edit: I guess instead of "power" I should have said "potential loudness."

[tekhedd]

So the question remains: how can I make my drummer play 10dB softer?

[fishtx]

Originally Posted by tekhedd

So the question remains: how can I make my drummer play 10dB softer?

Xanax

[Thunderthumbs73]

Originally Posted by okcrum

Thoughts?

At the risk of potentially getting into a "conversation" where the unsaid position on the outset is "I'm 'right' unless you prove to me beyond my ability to refute it, that I'm 'wrong'", I do wonder about the nature of frequency range and the notions that bass frequencies seem (or in actuality) to require much more power to be as audible to the human hear than higher, treble frequencies. That said, I don't hear/read this phenomenon explicitly addressed in your message, as to whether, as you say (or seem to say) that it takes three times the power to sound twice as loud to the human ear is equally applicable (and true) for every single frequency, or not?

Or in short, is the three times the power rule (as perceived by the human ear) applicable for every frequency, or not?

If so, then I stand corrected. If not, well... ...it would seem to me that "how much power" is a sliding scale is affected by frequency (among other things), and there can be no finite answer to the question unless we go one frequency at a time and speak in those kinds of specifics.

Or maybe I missed something?

[Thunderthumbs73]

I have hunches and suspicions and thoughts about things, but two things in this conversation I have experienced are true based on past experience, as far as I can tell it is:
a.) billfitzmaurice is a sharp, sharp tack.
b.) I'm no science genius.

And sometimes on a good day, I can even describe A Fletcher-Munson curve without loosing the individual I'm talking to.

Today might not be that day.

[Thunderthumbs73]

Originally Posted by tekhedd

So the question remains: how can I make my drummer play 10dB softer?

Brushes.

[mongo2]

Mine goes to 11.

I win.

[okcrum]

Originally Posted by billfitzmaurice

Those 'old wives' were the audio engineers who invented the decibel scale. The 10dB differential that on average is required to sound twice as/half as loud isn't something that was decided on lightly.

If you describe your dB formula as 10 x log(base 2)P1/P0 I agree. But this is not the engineering dB formula for power, which is a base 10 log. It's the psychoacoustic formula.

That's the crux of the issue. There are at least three different formulas for dB: Flux (power, SIL), field (voltage, SPL) and perception (psychoacoustic).

That's what I'm trying to clear up, Bill. I've been around the business awhile too, and I've met and talked about design issues with a few of those oldtimers.

Yes, it is. This also came about by design. It is imperfect, as it assumes a speaker that remains linear, and none do, but all that means is that once speaker thermal and mechanical power compression sets in it takes even more than 10dB more power to get 10dB more SPL.
Incorrect. See above.

Well, actually it is if you use the SPL formula

SPL = 20 x log(base 10)P1/P0 for SPL

and

P = 10 x log(base 10) P1/P0 for amp power in watts.

Those have been the formulas for those quantities since dB and those quantities were invented/discovered.

And that's part of the source of confusion. I think people freely interchange units which are not directly comparable, on top of having a subjective scale (psychoacoustics) superimposed.

Would you seriously advise someone with a 500 watt amp that (assuming his cab handled it which it won't) they'd need 5000W to sound twice as loud?

I'd be perfectly happy to accept that it takes 10 psychoacoustic dB to sound twice as loud, since that is the formula. But those dB in no way map 1:1 to electronic power dB or SIL dB.

[KJung]

Originally Posted by okcrum

If you describe your dB formula as 10 x log(base 2)P1/P0 I agree. But this is not the engineering dB formula for power, which is a base 10 log. It's the psychoacoustic formula.

That's the crux of the issue. There are at least three different formulas for dB: Flux (power, SIL), field (voltage, SPL) and perception (psychoacoustic).

As an interested layman, of course the 'psychoacoustic' definition of db's is what everyone is talking about. If a human can't perceive it, it doesn't functionally exist and, at least in musical instrument amplification, doesn't much matter.

It takes a lot of power (and speakers) to make things 'sound a lot louder'... hence when you compare the linear power scale to the log db 'perceived volume' scale (which IMO is the whole point), you get the 10 times increase on the linear scale equals a doubling on the log scale.

That is also why a 5db increase sounds HUGE (i.e., adding a second identical cab and halving the nominal impedance resulting in an almost doubling of amp power and a doubling in speakers). It is surely not a 'doubling', but it is a darn lot!

[okcrum]

Originally Posted by Thunderthumbs73

At the risk of potentially getting into a "conversation" where the unsaid position on the outset is "I'm 'right' unless you prove to me beyond my ability to refute it, that I'm 'wrong'", I do wonder about the nature of frequency range and the notions that bass frequencies seem (or in actuality) to require much more power to be as audible to the human hear than higher, treble frequencies. That said, I don't hear/read this phenomenon explicitly addressed in your message, as to whether, as you say (or seem to say) that it takes three times the power to sound twice as loud to the human ear is equally applicable (and true) for every single frequency, or not?

Or in short, is the three times the power rule (as perceived by the human ear) applicable for every frequency, or not?

I deliberately left the equal loudness curve and ear sensitivity part of the discussion out, because I knew I was opening a can of worms as it was.

I guess the simple answer is that for a given range of frequencies, you still need to compensate for the sensitivity of the average human ear. This doesn't affect the relative perception of "twice as loud" at a given frequency and sound level, but it does affect the power you need to balance the perceived loudness across the audio spectrum.

I think more what I was doing is trying to get an answer to the question I've asked several times here already. In all the previous posts, there was no answer, sad to say.

So far, I think you can see the answers to this post don't seem to clarify the issue a whole heck of a lot, either. I'm sure I'll see many more pronouncements of the rightness or wrongness of what I wrote, with or without any backing facts.

I'm hoping for a few answers with cogent arguments, not ad hominem attacks.

If so, then I stand corrected. If not, well... ...it would seem to me that "how much power" is a sliding scale is affected by frequency (among other things), and there can be no finite answer to the question unless we go one frequency at a time and speak in those kinds of specifics.

Or maybe I missed something?

No I think you got that, since I'm trying to simplify the issue enough for general discussion without reducing it to absurdity.

I'm trying to understand the 10 times the power rule. I personally don't think it's correct, though I'm willing to be shown that belief is wrong.

So I checked out the various definitions of dB, power, SPL, etc. and tried to relate them in some meaningful way along with the psychoacoustics, to try to figure out where that rule came from. It never seemed to make much sense to me, and I never even heard anyone in the business claim that until I came to TB. And that's what raised my hackles. I've been been playing bass for a long time, and also done engineering in the broadcast/recording business for almost as long since getting my EE. It's not like I just pulled my skepticism out of the air.

[s_mcsleazy]

ok this seems like a nerdalicious thread for people who actually reserch this

so im intrested

[SnakeKappele]

Originally Posted by Jim Carr

I think most of us say 1000 watts is twice is much power as 100, not that it is twice as loud, though no doubt we goof at times. So? Close enough for horseshoes, hand grenades, and bass rigs, IMHO.

I say 200 Watts is twice as much power as 100 Watts.

[s_mcsleazy]

Originally Posted by SnakeKappele

I say 200 Watts is twice as much power as 100 Watts.

and we have a winner

[Bassdirty]

[okcrum]

Originally Posted by KJung

As an interested layman, of course the 'psychoacoustic' definition of db's is what everyone is talking about. If a human can't perceive it, it doesn't functionally exist and, at least in musical instrument amplification, doesn't much matter.

It takes a lot of power (and speakers) to make things 'sound a lot louder'... hence when you compare the linear power scale to the log db 'perceived volume' scale (which IMO is the whole point), you get the 10 times increase on the linear scale equals a doubling on the log scale.

That is also why a 5db increase sounds HUGE (i.e., adding a second identical cab and halving the nominal impedance resulting in an almost doubling of amp power and a doubling in speakers). It is surely not a 'doubling', but it is a darn lot!

Agreed! I am actually admitting in this post, if you've seen any of my others on this, that I was wrong in purely taking an engineering standpoint, and tried to reach some reasonable conclusion based on psychoacoustics. I know psychoacoustics is not mumbo-jumbo, ever since I had to implement .mp3 protocol in software in the mid-90s.

Problem is, there is so much room to (mis)interpret not only numbers and physics concepts, but what our ears and brain tell us. I wouldn't expect to reach consensus here, I'd be happy to understand why Bill and others think as they do, and agree to disagree if necessary in a respectful manner.

[KJung]

Originally Posted by okcrum

Agreed! I am actually admitting in this post, if you've seen any of my others on this, that I was wrong in purely taking an engineering standpoint on this, and tried to reach some reasonable conclusion based on psychoacoustics. I know psychoacoustics is not mumbo-jumbo, ever since I had to implement .mp3 protocol in software in the mid-90s.

Problem is, there is so much room to (mis)interpret not only numbers and physics concepts, but what our ears and brain tell us. I wouldn't expect to reach consensus here, I'd be happy to understand why Bill and others think as they do, and agree to disagree if necessary in a respectful manner.

+1 I'm way over my head, but interested in how all this works. When I see anyone in the musical instrument amplification world talk about db's, I always assume it is the 'psychoacoustic' non-linear scale, since that is what we as musicians, sound reinforcement pro's, and amp manufacturers, etc. deal with.

Of course, in the real world it gets more muddled, since 'published power' is surely not an exact measurement on an amp spec sheet (different THD, different frequency ranges, different distortion levels in preamps, etc,etc.), and of course a speaker cabinet adds so many confounding variables that it is very difficult to determine what impact all this stuff is having (the wonderful world of complex, non-linear interactions among different components)!

Fun discussion. I always learn a bit.

[s_mcsleazy]

ok but honistly it kinda reminds me of the bugatti veyron in some ways

because when they made the veyron super sport they only managed to make it go like 10mph faster than the previous one even tho it had 200bhp and was alot lighter

now lets say that in this arguement that power is the bhp

the veyron could only go the extra 10mph faster even with all that power/lightness because when moving at that speed the air is thicker so cant the same thing be said for sound. sound too is limited by the air too?