The ear does process SPL in a logarithmic fashion and works roughly like this.
The smallest change in SPL that can be heard by a 'normal' person is 1dB. Many need a 2dB change to be positive and this is with a test signal.
A clearly percieved increase in level on a music signal is probably closer to 3dB, depending on how the test is done.
A 6dB increase in SPL requires a doubling of amplifier power, a 10dB increase requires 10 times the power, OK so far?
This has implications. For example, a pair of averagely sensitive speakers, say 89dB (1watt, 1meter) produce roughly that level at a normal listening distance in a normal room, this is loud, a more normal 'serious' listening level is around 79dB, requiring 0.1watt, not very much you might think.
So let us play a quality modern recording with a dynamic range of 60dB, remember a CD has a theoretical 96db range. Assuming the average level is 79dB then the average power required from the system is just 0.1watt. Peak level however is 30dB (half of 60dB) higher, ie 10 x 10 x 10 times higher, 100watts in this case.
So you have some new music, or a new bit of kit and invite a few friends round to show off and you turn it up a bit, another 6dB and we are talking 200watts and that is before you build in anf headroom, a professional system will usually have 3 - 6dB, sometimes more.
Choose a less sensitive model, a PMC or a small ATC and a 200watt amplifier is barely adequate and if you are having a party, just forget it.....
Quick and dirty admitedly, but it does give you an idea of what power is required to make a hi-fi system work.
Playing devils advocate, if all of the above is true, why is it that so many people are happy with much less than 100W amplifiers, 50W even? also, there are many even less powerful valve amplifiers.
Are the owners of such low powered amplifiers always listening at much reduced volume levels, or are the amplifiers in a state of or near perpetual clipping?
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Measured levels in the home hi fi environment are often much lower than you might think, until you turn it up!
A lot of low powered amplifiers are running close to the edge and how they behave in those conditions may explain the audible differences between them. This applies to both valve and solid state components.
The maxin that 'all competant amplifiers operating within their design parameters sound the same' is probably true, the clue is in the words in italics.
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Overdose, in my case the answer to your question is speakers that are about 103 dbs/2.83v/1m efficient. Amplifier power for home listening becomes academic with speakers like this. The speakers are also only about 1 db down at 20hz. Any music or film sound tracks with bass content have real physical impact when peaking over 90dbs, let alone 100dbs or 110dbs!
Davedotco a 6db increase in Sound Pressure Level (SPL) requires 4 times the power, not twice. A 9 db increase require 8 times the power and as you quite rightly said 10dbs requires 10 times the power.
If you or anyone is listening so that the average level is 79dbs and peaks are 30 dbs above that, ie 109dbs, then you are listening very loud. So loud that you're at risk of permanently damaging your hearing. You're likely to have ringing ears after listening at these levels.
When I listen at levels where the peaks are at 80dbs and therefore the average levels with a good dynamic recording are at 50 dbs, this still sounds like a generous volume.
And something else to bear in mind is how many dbs drop-off you get between 1m from your speakers and your listening position. I get about 10dbs drop-off in my room.
3 db more power is 2x200 instead of 2x100
6 db dosn't mean that if you have 2x100 and increase the output from the amplifer with 6 db that it's 2x200.. an increas of 6 db is in watt 2x400
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And Overdose, if you're using a typical solid state amp and it's in a state of being perpetually close to clipping, then that's a good thing, because these amplifiers have their lowest levels of THD+N distortion as a percentage when they are close to clipping.
Of course total system THD+N distortion is then likely to depend on the speakers and frequency content of the recording. If you have a modest 20 watt solid state amp playing at levels where 10 watts are being drawn from it then it's highly likely that the speakers will be producing far more THD distortion than the amplifier, especially in the bass region.
I'm familiar enough working with log ratios in dBs or when referenced to an absolute quantity such with the dBm but equating perceived loudness is far from intuitive to me. I can understand how human's frequency response is measured by switching between a fixed tone as the reference then a stepped tone of perceived equal loudness with the results averaged over several people then repeated according to age but what is twice as loud really mean?
Half power has been mentioned as used with frequency response measurements but that refers to power or amplitude, not loudness. The level difference of 10dB seems to be the agreed amount - not 3dB I'd thought it was.
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3db, 6db and 10db are all correct, it depends what you are measuring. There is an interesting explanatio here: http://www.sengpielaudio.com/TableOfSoundPressureLevels.htm
Didn't get most of it, but the table down the bottom explains things.
There doesn't seem to be a lot of agreement so far. Several different 'definitive' answers.
60db of dynamic range in a recording! I think this is a little extreme, from recollection in a thread a few months back where one user was posting the analysis of some linn hd recordings, I think the best of these was only around 14db, unless you are including the silence at the beginning and end.
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this will be about right I would guess unless you happen to listen 1m from your speakers, the room Coustics will also play a part as an overly bright or reflective room will sound louder due to the energy being reflected and ot absorbed by furniture etc
The rating of amplifiers is for a continuous output (100w for example) however most amplifiers will produce much higher power than this for short periods (milliseconds) which is all that is required to cover musical peaks, (The average power required is usually pretty low) and this is why amplifiers seem underpowered on paper, but work fine in the real world.
Hope this helps
14db maybe typical on many recordings but is far from the best, even Led Zepp have 35db on Stairway, classical music is often far more, going from very quiet to full orchestra.
As I said in my original post it was a 'quick and dirty' attempt to give an overall impression of what is going on, any competent engineer can pick any number of holes in my calculations. I does however give the average hi fi owner a glimpse of what is actually going on. It was pretty much off the top of my head so some of my figures could be off, but the overall gist of the piece is realistic.
It is far more complex of course, as several people have pointed out. Two of our 89db/watt speakers produce 6dB more than one if they are playing the same signal, but for a stereo music signal it is a little less, similarly room gain will have an effect of lifting the level at the listening position but the usual listening position is more than 1 meter from the speakers so I have chosen to assume that they roughly offset one another, which they do.
Similarly while it is true that most commercial recordings (even good ones) have very limited dynamic range, well recorded acoustic intruments can have a quite enomous range. Also, as was pointed out a 79dB average SPL is damned loud if you are listening in a normal size room on your own, but a bigger room and a few people make an enoumous difference to the power requirements.
As always with subjects of this type it is too easy to get overwhelmed by the detail and complexity of the situation but the reality is this;
If you have speakers of average sensitivity in a 'normal' size domestic room and play at reasonable levels then a 50 watt amplifier is propably going to be fine, but step outside those parameters and all bets are off.
I'm not yet convinced that "twice as loud" or "half the volume" are quantifiable. I can get to grips with "equal loudness" as a valid perception but "double" or "half" is like saying the bath water is now "twice as hot" as it was before. It's not an absolute like saying "I'm now sitting twice as far from my speakers".
It does make perfect sense to refer to a doubling of loudness to definable quantity such as power for the convenience of measurement but is arbatory rather than absolute. Length seems like an absolute primary quantity but it is now defined by the speed of light & a time interval rather than the intuitive to understand physical metal bar with markings 1m apart!
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