Just to quickly interject on the confusion of 3 dB/ 6 dB/ 10 dB/ etc. (and to hopefully not make the confusion any worse
), let's remind ourselves about decibles and how they relate the amplitude of signals.
dB = decibel = 1/10 of a Bel
Bel = Log[ value / reference ] (Here, 'Log' means Logarithm base 10.)
Therefore, the value in dB of some signal is given in relationship to a reference as 10* Log [ signal/reference ]
A Bel is a unitless measure of amplitude on a logarithmic scale. It is given in terms of a reference value. Not all decibel measures are equal, due to differences in the reference value.
For example, the amplitude of an electrical signal may be given in dB amplitude ("dBu") or dB power (simply "dB"). This is a frequent source of confusion, because folks often think in terms of the voltage amplitude of a signal; however, folks also often think in terms of the power of sound. The problem arises because the voltage sent to audio transducers is typically related to the sound pressure; however, the power of the electrical signal and the sound wave are proportional to the voltage-squared and the pressure-squared, respectively. One can see how this leads to a factor of two difference between the dBu and dB ratings for the same signal.
Lets say the voltage amplitude is V and is being driven across a load with impedance R. Furthermore, lets use a reference voltage amplitude of V_ref.
(Recall P= V^2/R)
Similarly, V and V_ref could be a pressure amplitude and reference, respectively. R would be the acoustic impedance of the the medium through which the sound is traveling, and P would be the power-per-unit-area.
dBu = 10 * Log[ V / V_ref ]
dB = 10 * Log[ (V^2/ R) / ((V_ref)^2/R) ]
= 10 * Log[ ( V / V_ref )^2 ]
= 20 * Log[ V / V_ref ]
Hence, a 1 dBu change (amplitude) corresponds to a 2 dB change (power).
When folks talk about a 10 dB change corresponding to a doubling in perceived volume, they're talking about 10 dB power. Here, the amplitude change is 5 dBu.
As far as base 10 is concerned:
- 10 dB corresponds to a change in power by a factor of 10
- ~3.01 dB corresponds to a change in power by a factor of 2 and a change in amplitude by a factor of sqrt(2)~1.41
- ~6.02 dB corresponds to a change in power by a factor of 4 and a change in amplitude by a factor of 2
Hope this helps clarify how dB differences relate to amplitude and power.
(Naturally, one might have googled this to find the wiki page on the decibel scale linked here for convenience
EDIT: errors fixed, thanks bigshot & wakibakiEdited by ab initio - 4/24/14 at 7:28pm