• 3dB = twice the power
• 6dB = twice the amplitude
• ~10dB = twice the perceived volume
• Adding up two 12dB noise sources will get you, on average, 15dB (which will not sound twice as loud)

I was working with a sound engineer and asked for a level to be dropped 3db. Their reply was “so you want it half as loud?” and I said “No, 3db” which was countered with “3db is half the volume”. So that’s what prompted me to look into decibel changes and how that translates to our real world perception.

It is true that to increase a volume level by three db requires twice the power, which I think is where the confusion is. A doubling in power does not equal a doubling in audio perception.

It was determined many years ago in controlled audibility testing, that the following rules were generally accurate among the population:

• 6dB SPL increase is perceived as an approx. 50% increase in volume by a sample group.
• 10dB SPL increase is perceived as an approx. 100% increase in volume by a sample group.

Another Explanation

A 3dB increase is twice as loud, in that increasing the level by +3dB by definition means twice as much audio energy is now being pumped into the room – well, actually 1.995 times as much, thanks to the wonders of logarithms. But the human ear’s response is also logarithmic, so twice the energy does not sound like twice the volume.

There is, of course, no clear point where anybody’s going to say “ah, that’s now precisely double as loud as it was before”; there’s no little mental VU meter needle. But the general rule of thumb is that people tend to call a 10X, or 10dB, increase in audio power “twice as loud”, if you insist that they indicate such a point, and this is backed up by neurological studies.

Every little 1dB step along the way, though, is noticeable (the general rule of thumb is that people can consciously notice a 1dB volume change, though a somewhat smaller increase in volume commonly causes people in both blind tests and hi-fi stores to think they’re now listening to a better system…), and having a whole lot of amplifier watts on call both makes sure that you’ve got headroom for sudden loud events and enough power to make the subwoofer shake the floor correctly.

For the super geeks, here’s the math:

For doublng of amplitude:

6dB: 20 * log10(2/1) = 20 * 0.3 = 6

In application, this has always held true as long as the vector of both correlated(in phase) SPL sources were localized to within a small proportion relative to the wavelengths examined). Sound pressure change is only an amplitude change.

Here is an easily illustrated electrical example of double amplitude = double power:

V * I = W(power)

Assume a 10 volt peak to peak AC signal @ 10 amperes/current.

10 * 10 = 100(power/watts)

Double voltage amplitude(voltage=20), same current/amperes:

20 * 10 = 200(power/watts)