Loudness and Speaker Sensitivity
Sound levels are measured in dB, decibels or tenths of a bel. In general, a level increase of 10 dB sounds twice as loud. The minimum detectable level difference is often said to be 3 dB. However, in situations like the members of a band trying to get the balance of instruments right as little as one dB may be significant.
The required power level doubles for each 3 dB difference. This means that, for example, going from a 50 to a 70 watt amp may not make much difference in maximum loudness; you'd need to go to 100 just to get a noticeable (3 dB) difference. A 10 dB difference requires 10 times the power. To sound twice as loud as 50 watt amp with the same speakers, you need 500 watts, assuming the speakers can take that.
Of course, music is not a steady-state signal. Usually there is a difference of at least 10 dB, sometimes as much as 20, between the average level and the peaks. Suppose the ratio on your music is 20 dB, you have an amp rated at 50 watts, and the average loudness level you want needs 3 watts. Peaks will need 60 watts; an amp rated for 50 watts continuous power would generally have enough extra capacity to handle the occasional peak at that level. (Perhaps not, though; it depends on details of both the amp and its power supply.) However, at some point -- either because parts of the music have more peaks or because you cranked the volume up -- the amp runs out of power and "clips" the signal. This produces one of the nastiest-sounding forms of distortion. It is also quite likely to damage speakers.
Going from a 50 to a 70 watt amp may not make the music much louder, but if it eliminates or reduces clipping it may sound a lot better.
Speaker sensitivity is usually specified in dB with 1 watt input measured with a microphone placed one meter from the speaker and on the speaker axis. There are complications. Most such measurements are done at a single frequency, often 1000 Hz; if the speaker has a peak or dip at that frequency, the results will be a little misleading. Also, for an 8 ohm speaker, 1 watt input is 2.83 volts. Do you measure a 4 ohm speaker at 1 watt (1.42 volts) or at 2.83 volts (2 watts)? The latter method gives a result 3 dB higher, and is therefore popular with marketers. Finally, while the method works well for almost any conventional driver, it does not apply very well for things like measuring the overall response for a 3-speaker system or a flat panel such as an electrostatic speaker.
That said, nearly every manufacturer gives a spec in dB @ 1 watt, 1 meter. They range from about 80 dB to a little over 100. Let us look at how that spec relates to required amplifier power.
For the sake of discussion, take 110 dB per speaker as our goal, 90 dB average loudness with 20 dB of "headroom" for the peaks. This is a commonly used number; enough for a home system, barring huge rooms, absolute head-bangers, and so on. If we could just buy speakers with 110 dB sensitivity, we'd only need a one watt amp. However those speakers don't exist, so we need more power. To be exact, for every 3 dB our chosen speaker's sensitivity is below 110 dB, we need twice the power.
110 dB -> 1 W, 107 dB -> 2 W, 104 -> 4, 101 -> 8, 98 -> 16, 95 -> 32, 92 -> 64, 89 -> 128, 86 -> 256, 83 -> 512, 80 -> 1024
For example, if speaker X has a sensitivity of 86 dB and you want 110 dB of loudness, you need about 250 watts to drive them. The first thing to check is the manufacturer's spec for power handling of those speakers; if they cannot take 250 watts (peak), you cannot use them. Then look at the costs and other benefits; would a higher efficiency speaker and a lower-power amp be a better choice?
So the designer has trade-offs and compromises to make. Some low-sensitivity speakers and some low-power amps are definitely worth using because they are excellent in other areas. However, if you choose both low-sensitivity speakers and a low-power amp, the system will not play loud. For some users, that is fine. If it isn't for you, you might use multiple amps and speakers -- two give you an extra 3 dB, four give 6 dB and so on. That is the only way to get a system that plays loud with low-sensitivity speakers and low-power amps; disadvantages are that it is expensive and it complicates the design. Other choices would be to use more sensitive speakers or a more powerful amp.
Contains numerous errors...
This was written under the misunderstanding Sound Pressure Level (SPL) was of the form 10 Log (P2/P1) which is not the case. This is true for Power not Pressure!
SPL is of the form 20 Log (P2/P1). This causes all of the examples and conclusions to be in need of revision.
Note: Log is base 10...
There is also recent work that suggests that TWICE the volume (twice as loud) may be closer to 6dB SPL rather than 10 dB SPL. This is a psychoacoustic observation and is difficult to quantify. In any event 6-10 dB is a more appropriate measure. 6 dB SPL is 3 dB Power which suggests that twice as loud requires a little more than twice the power, but less than 3 times.
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