Courtesy of DocFoster

Well at least that's what I'll try to do.

There�s been a few threads on hififorum lately that have been exploring the meaning of and the relationships between the ratings for speakers and the ratings for amplifiers.
There�s also been some well made points about the ineptitude of the hifi press.
These 2 issues have got me thinking�
The situation regarding amp power vs amp loudness vs speaker specifications vs system loudness is indeed complicated. It is also important to the sound of a system. Perplexingly I have rarely, if ever, seen it explained, or even discussed in the hifi press. Amplifier wattage figures and speaker sensitivity are listed, but their meaning is left shrouded in secrecy. This neglect of duty on the part of hifi publications is perplexing because of the importance of speaker and amplifier specifications to the overall sound of a system. If I was being cynical I might suggest that this can be explained by pointing out that the hifi press is servant to �the industry� and not their paying readership. But I�m too much of a na�ve optimist to suggest that.

The specs for amps and speakers are so important because they do have an influence on the �dynamic range� of a system. And dynamic range matters.
There is more to hifi than dynamic range of course. A flat frequency response for one. But at reasonable listening levels, the relative loudness of the attack of snare, or of the resonance of double bass, or of the initial consonant of a vocal line or of the crescendo of an orchestra is a crucial part of the faithful reproduction of the original source. If a system cannot faithfully reproduce the original source for the listener, the experience will not be a hifi one. Thus dynamic range must be seen as a crucial part of the hifi mix.
Now, component specifications do have direct bearings on the dynamic range of a system, but there�s more to getting a good dynamic range than simply buying the amp with the highest wattage figures.
To illustrate this, I do have some information that may move our discussions on a stage.

The confusion over power ratings (in Watts (W)), and sensitivity for speakers ratings in (Decibels (dBs)) is understandable as without knowing how to put them together the figures are useless. I�ll do my best to explain what I know below by working through the following important areas.

1. Firstly I�ll discuss the important variables that affect the potential loudness and dynamic range of a given system:
Amplifier power in Watts and more importantly amplifier power decibel Watts;
Speaker impedance in ohms an;
Speaker sensitivity in decibels.
2. Secondly I�ll outline how the listening distance from the speakers in metres affects the perceived dynamic range of the system.
3. Finally, I�ll try to explain my understanding of how these variables come together to affect the dynamic range of a system.

I�ll start at the beginning of the amplification chain: The amplifier itself. It�s important to understand exactly what the amplifier�s power in watts actually means for a system�s dynamic range. This is only a little complicated.

Point 1: Amplifier power in watts and speaker impedance in ohms.
An amplifier�s power in watts is the amount of electrical power that the amplifier can deliver to the particular speaker to which it is connected. As a will discuss below, talking about power is very much not the same talking about loudness.
The first point that requires clarification is that an amp�s power in �Watts� is dependent on the impedance offered by the particular speaker in use, measured in �ohms�. Many of you will know about this already, and may wish to skip to point 2.
Most amplifiers give their power rating when driving an 8ohm speaker (e.g. �80 watts into 8 ohms�). However, many speakers have a lower impedance than this (e.g. 6 or 4 ohms).
Here the important thing to know is that essentially the lower the impedance of the speaker the higher the number of Watts the laws of physics will command the amplifier to deliver. If the impedance is halved from 8ohms to 4ohms, the Watts could as much as double (i.e. from 80 to 160 Watts), although (for reason that I don�t fully understand,) this it is usually less than simply double the power.
This potential doubling of power output is not always a formality for the amplifier. I�ve got a friend whose bargain basement amplifier simply couldn�t cope with a 4ohm speaker load and kept trip-switching out at anything above extremely quiet listening levels. Not all amplifiers have a �low impedance driving capacity�.
The important things to remember when looking only at the Watt rating of an amplifier is firstly that the speakers impedance will directly affect the amps wattage output.
But more than this, resulting wattage is in itself meaningless when considering �how loud� a system will sound or what its dynamic range will be. To fully understand the role of raw Watts of power to the dynamic range of a system the watts figure must be converted to a figure for �power loudness� in �decibel Watts�. Here we go�

Point 2: Amplifier power �loudness� in decibel Watts (dBWs).
The first of these considerations is that as amplifier power in Watts doubles, loudness does not. The progression is not linear. This is because ears perceive the volume of sound as changes in sound pressure. To double the pressure exerted on the ear, a speaker requires to be fed with considerably more than double the power.
This sound pressure / loudness business deals in the currency of decibels (dBs). Thus any talk of �loudness� or �dynamic range� must be in the context of dBs.
The conversion table below shows how an amplifier�s raw �power� figure in simple Watts relates to its �loudness� in decibel Watts (dBWs):

Amp power in Watts and their equivalent amp loudness in dBWs:
10 = 10
20 = 13
50 = 17
63 = 18
79 = 19
100 = 20
126 = 21
156 = 22
200 = 23
251 = 24
316 = 25
400 = 26

You will notice that to double the �loudness� of a 20 Watt amplifier one would have to upgrade to a 400 Watt amplifier (i.e. 20 times more powerful). As mentioned above, whenever decibels are involved, the power situation is never a linear one.

Even after having made the conversion for the amplifier from power ratings to loudness ratings, there are more variables to consider when gauging the overall dynamic range of a hifi system. The loudspeakers will have there own decibel ratings�

Point 3: Speaker sensitivity in decibels (dB).
This bit is simpler but just as important.
Basically a speaker�s �sensitivity� is determined by how many dBs a speaker produces when supplied with just 1 Watt of power, measured at 1 metre from the speaker. (The distance is important for reasons that will be outlined below.)
Thus, with a given power output a speaker with a sensitivity rating of 90dB is �louder� than a speaker with a rating of 86dB. This is why lower powered amps (e.g. valve amps) are considered to be �more compatible� with higher sensitivity speakers: A higher sensitivity speaker will be heard as louder, and so have a larger dynamic range with a given amplifier than a lower sensitivity speaker.

Point 4: Listening distance in metres.
Even easier, and surprisingly important!
It is intuitively obvious that the further away the listener is from a sound source (e.g. a loudspeaker) the quieter it becomes to the listener.
A figure can be put on this factor. Essentially for every metre away from a loudspeaker the listener moves 5 decibels of loudness are lost.
For instance, using the example of a speaker with a sensitivity rating of 86dB (already measured from 1m away remember), if one was listening to that same 1 Watt input from 4m away, the listener would hear 15dB less (3x5dB for the additional 3m distance), i.e. 71dBs.
Basically the closer to the speaker the ear is, the louder the music sounds.
This is a very important point. One does not read in the hifi press about listening distances. And yet this factor is at least as important a determining factor on loudness / dynamic range / peak listening levels (choose whichever term you find most appropriate) as the amplifier and speakers themselves. More of this below.

Point 5: Peak listening level in dBs.
I hope that its reasonably clear from what been written above that the effective loudness (or �dynamic range� or �peak listening level�) of a system is affected by several factors, namely:
1. Amplifier power in Watts and more importantly amplifier power decibel Watts (taking into account speaker impedance in ohms);
2. Speaker sensitivity in decibels and;
3. The listening distance from the speakers in metres.

For me, the precise way in which these can be brought together to calculate a system�s loudness / dynamic range / peak listening levels (choose whichever term you find most appropriate) is the interesting part. The interesting, but contentious part.
To perform this calculation I�ve come across an equation to determine the peak listening level of a given system at a given distance. The equation was included in a piece of literature published by Musical Fidelity. I am prepared to take the equation at face value (call me �Dr. Gullible�), but it also seems to make logical sense. However, as I�ll illustrate later, the equation does have some surprising implications.
In any event, using the factors discussed above, the equation is simple enough to operate:

Where x=sensitivity rating of speakers in dB
y=amplifier power in dBW (not simple Watts)
z=distance from speaker in metres

The dB peak listening level = x+y-5(z-1)

(Remember that the �5� comes from the 5dB loss for every metre moved away from the speaker and the �-1� allows for the fact that the speaker�s dB sensitivity was measured at a distance of 1m).

For any equation it�s always useful to work through some real figures. For my system this is as follows:

For �x�: My Dynaudio Audience 82 speakers are rated as 87dB sensitivity.
For �y�: My Musical Fidelity A3.2 amp claims 185 watts into the 4 ohms (the impedence figure for the Dynaudios). Using the conversion table above, this figure equates to somewhere in between 22 and 23dBW. I�ll call it 22dBW
For �z�: I listen from approximately 3m away from my speakers.

So, my peak listening level = 87+22-5(3-1)
= 87+22-10
= 99dB

I�ve read somewhere that a figure of �100dB� for peak listening levels is the benchmark to aim for, so I suppose 99dB isn�t too bad.

As mentioned above, some surprising issues come out of this equation:
Firstly the fact that by moving one�s listening position forward by 20cm, one would have the same affect on peak listening level as would increasing speaker sensitivity by 1dB. Indeed, based on the above calculations, I could achieve the magic �100dB� figure simply by leaning forward slightly (20cm to be precise).
From a personal point of view, musing on this equation has made me think further along this train of thought: I�m hoping to move home to a larger house soon and I�m hoping for a larger and more dedicated hifi room. However, on the basis of the above equation, if a larger listening room also means a longer distance between my speakers and my ears (perhaps an additional metre), then this will have a detrimental affect on the peak listening level of my setup. A significantly detrimental affect: A decrease in peak listening level of 5dB. To compensate for this 5dB change by increasing my system�s amplification is relatively a huge task � in the case of my amp, I�d have to step up by around 400watts to 500watts per channel! There are domestic amps that can achieve this (e.g. the amps at the top end of Musical Fidelity�s own KW range), but they are a dramatic and pricey upgrade.
Alternatively I could reclaim the 5dB lost in the extra metre in front of my ears by changing my 87dB sensitive speakers to transducers of 92B sensitivity. Again, such products do exist, but they are few and far between.

Conclusions:
I�m not really sure what to make of this. That such change in dB peak levels can be affected so radically by apparently small changes to listening distances seems counter intuitive. Having said that, try moving your head towards and away from your speaker by a metre � the difference in dynamics is significant. I�d be interested to read opinions on this from other hififorum users, or from technically minded people.

In any event, I hope that what all this shows is that the ways in which we listen to and enjoy our hifi�s generally and their dynamic abilities (including volume) specifically is dependent on how a whole raft of issues come together.
Essentially those crucial moments of loudness (the relative loudness of the attack of snare, or the resonance of double bass, or the initial consonant of a vocal line or the crescendo of an orchestra) are experienced by the hifi listener as sound pressure (in dBs!) on the ear and not by the hifi buyer as watts in the amplifier�s manual. If the appropriate sound pressure is not applied to the ear (i.e. if the amp is too feeble and/or the speaker to insensitive and/or the ear is too far away) the sound be experienced as compressed, unnatural and disappointing � and certainly not as a hifi one.
Amplifier power in Watts is an issue, but so is speaker impedance in ohms, speaker sensitivity on dBs and listening distances in metres.
The sooner the popular hifi press recognises and writes in the context of such issues (rather than simply prattle on about the �openness� provided by a particular isolation platform) the sooner they will become credible to us hifi lovers who will then be able to make more informed decisions about our hifi setups and listening areas.

This FAQ entry courtesy of DocFoster