Something I wrote on the subject, oh and its +10dB SPL to double the percieved loudness.
There are many ways to talk about and explain sound. We can say it is dry, flat, bright, dull, muddy, brilliant, and many other descriptions. Terms such as that are intangible when it comes to the next guy, one man’s perfect sound, is another's mud. These kind of descriptions can be helpful and can be used as a basic guide, but other terms like a dB (deci-Bel) can be given an exact scientific definition. Knowing what such terms mean is helpful, not just for helping us to pick out and compare components, but it also helps to understand how we hear.
A Bel is a standard of measure, named after Alexander Graham Bell. A deci-Bel is one tenth of a Bel. So what is a Bel? Well, a Bel is the logarithm of an electrical, acoustic, or other power ratio, the key being power. The formula for this is Bel=log(A/B) with A and B representing the two levels being compared. Since, in sound issues, a Bel is really too large a number to work with, they wanted to use something smaller and went to a dB, which changes the formula to dB=10*log(A/B). To help put this in non-tech terms, dBs are used to measure how much more or less we have of a certain thing. In this case how much more or less of an acoustic power or signal level, referenced to a certain level. dBs can be used in a variety of situations when talking about our gear, whether it is voltage, wattage or SPLs(Sound Pressure Levels). I will point out that a dB is a dB, whether it is talking about volts, watts, or SPLs, how we figure the ratios is somewhat different, but in the end a 1dB increase in voltage, is a 1dB increase in wattage, is a 1dB increase in SPLs.
Now to apply this to our electronic gear, first comes voltage. I start here because this is ultimately what drives our speakers and components. It is also the one that throws a curve ball at us in relation to the formula. Now if you know Ohms Law, you know that power is proportional to the square of the voltage. Since the dB(power) = 10*log(A/B) formula is for power ratios, the voltage formula changes to dB(volts) =20*log(A/B). Let’s apply this to the real world. The average home stereo CD player puts out about 2V (volts) with the maximum signal recorded on a CD. With the 2V given, if I said that a particular CD' s average level output on the same CD player is about .6V, how much below the peak level of 2V would the average be? 20*log(2/ .6)=10.4 dBs. This is just a small example. The point is that if you know two voltages you can determine the difference in dBs. Also if you follow the formula, doubling the voltage will yield a 6dB increase, but this is not so with wattage.
How do dBs correlate to wattage? Well, since watts are a measurement of power, we can go back to the dB= 10*log(A/B) formula. When looking at receivers and power amps, marketing and salesmen types love to throw out numbers like this or that has this many watts, but it really means nothing until you get that broken into dBs. Take an 175 watt per channel amp, and a 250 watt per channel amp. Based just on the manufacturer’s specs we can determine the exact difference in dBs between the two. Before we do, I want to make it clear that just because there might be the smallest of differences in dBs does not automatically mean that the component with the smaller wattage is just fine. It should come down to how clean one sounds over the other. Ok, putting in the above numbers you get dB=10*log(250/175). That calculated out equals 1.55dBs, not much difference at all. To get a noticeable perceived difference in volume, you need about a 3dB increase; 1.55dBs falls well short of anything significant.
That leads us into the discussion of dBs and SPL. The human ear needs that 3dBs more to perceive a noticeable change in volume, and to perceive a doubling in loudness we need an increase of 10dB. Now going back to wattage for a moment, to get 10dB more in terms of watts, you need ten times the power. While you digest that for a moment, you also need to know how speakers are rated in relation to dB SPLs. A speaker usually has a rated sensitivity somewhere in the manufacturer’s specs. This measurement as an industry standard is taken with a 1 watt input at 1 meter away on axis with the tweeter. The average is about 90dBs. That tells us with one watt of power at one meter away the speaker will produce a SPL of 90dBs. So if the same speaker is driven by a 100 watt amp, you would use the following formula dB= 10*log(100/1), the 100 being the one hundred watt amp, and the 1 being the one watt to obtain the given sensitivity. With that plugged through the calculator, you come up with 20dBs. That, in turn, means that if this speaker is driven with 100 watts of power, it will reach 110dBs at one meter away. The relation of dBs and distance can also be used to help determine how loud that 110dBs might be at say twice the distance. This falls under the inverse square law. Basically, all you need to know is that in a reflective-free environment, if you double the distance you lose 6dB of sound pressure. So at 2 meters that 110dBs is now only 104dBs,but in the real world we don't live in a reflective-free environment so the drop most likely won't be exactly 6dB.
To close, a few things are very important to remember about dBs, volts, watts, and SPLs. First, just because one power is higher than the next, does not mean it is significant, but at the same time if the lower-powered device does not sound as good as the higher-powered one, the difference in dBs won't matter either way. Also remember if you are dealing with manufacturer specs, the variance of some manufacturers overrating their equipment's ability or in some cases underrating its ability needs to be factored in. Next, the more headroom the better. How and where dBs are referenced to is also important. When I say a SPL meter reads 90dBs, that means that a sound is 90dBs above the threshold of hearing. With CD's, Full Scale Digital (a maximum recorded signal) is referenced to 0dB. Anything below that becomes a minus dB from the stated reference point. In the long run, it helps to remember where the reference point is. Understanding dBs and how they relate to our components, speakers, and ears is important, and I hope this humble column has started or increased your knowledge on dBs.
