Digital Sound & Music: Concepts, Applications, & Science, Chapter 4, last updated 6/25/2013
29
( ) increase in voltage
It’s worth pointing out here that because the definition of
decibels-sound-pressure-level was derived from the power decibel
definition, then if there’s a 3 dB increase in the power of an
amplifier, there is a corresponding 3 dB increase in the sound
pressure level it produces. We know that a 3 dB increase in sound
pressure level is barely detectable, so the implication is that doubling
the power of an amplifier doesn’t increase the loudness of the sounds
it produces very much. You have to multiply the power of the
amplifier by ten in order to get sounds that are approximately twice
as loud.
The fact that doubling the power gives about a 3 dB increase
in sound pressure level has implications with regard to how many
speakers you ought to use for a given situation. If you double the
speakers (assuming identical speakers), you double the power, but
you get only a 3 dB increase in sound level. If you quadruple the speakers, you get a 6 dB
increase in sound because each time you double, you go up by 3 dB. If you double the speakers
again (eight speakers now), you hypothetically get a 9 dB increase, not taking into account other
acoustical factors that may affect the sound level.
Often, your real world problem begins with a dB increase you’d like to achieve in your
live sound setup. What if you want to increase the level by ? You can figure out how to do
this with the power ratio formula, derived in Equation 4.11.
( *
( *
Thus
Equation 4.11 Derivation of power ratio formula
It may help to recast the equation to clarify that for the problem we’ve described, the desired
decibel change and the beginning power level are known, and we wish to compute the new
power level needed to get this decibel change.
Equation 4.12 Power ratio formula
( *
(

)
Aside:
Multiplying power times
2 corresponds to
multiplying voltage
times

because
power is proportional to
voltage squared.
Thus
3 dB increase.
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