Digital Sound & Music: Concepts, Applications, & Science, Chapter 4, last updated 6/25/2013

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( ) 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.