# Amplifier power and volume.

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#### Pepsiiuk

##### New Member
Hey,

Sorry to bring up the topic of the dreaded decibel again but I’m a bit stuck on the subject regarding amplifier power and volume (SPL).

I have been told that you need 10 times more power to double the volume of a speaker but I don’t quite understand why. I know ears work in a log scale but I can’t seem to link everything together.

Thanks.

##### New Member
A(in dB) = 10 log A

where A is the gain
does this make any sense?

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#### Pepsiiuk

##### New Member
A(in dB) = 10 log A

where A is the gain
does this make any sense?
It does but thats part of the problem. Ive alsways understood that a 3dB increase is double the original. But going back to needing 10 times more power, 10 log (10/1) = 10 not 3.

Thanks

##### New Member

log (10) = 1

log(100) = 2

so the gain 10, 100 etc are getting multiplied by 10 each time while the ear detects the gain in dB which is 1, 2 etc...
i.e for the sound to be twice as loud the actual gain must be increased 10 folds; 10 times the initial power is required

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#### MikeMl

##### Well-Known Member
Hey,

Sorry to bring up the topic of the dreaded decibel again but I’m a bit stuck on the subject regarding amplifier power and volume (SPL).

I have been told that you need 10 times more power to double the volume of a speaker but I don’t quite understand why. I know ears work in a log scale but I can’t seem to link everything together.

Thanks.
Here are the assumptions that need to be discussed:

If Power1 into a given speaker produces a SoundPressureLevel1, does doubling the power produce an SPL2 which is double? (I say yes)

Does SPL2 sound twice as loud as SPL1? (I say yes, but I'm less certain)

Doubling power to the speaker is a 3 db increase,
e.g. 10*log(8/4)=10*0.301≈3.

Does this sound twice as loud?

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#### crutschow

##### Well-Known Member
The perception of sound levels is quite subjective. Most studies indicate that a 3dB change is barely perceptible and a 10dB change causes a doubling of the perceived level.

That is why a 3dB variance in a speaker response with frequency, although appearing to be significant, is not that noticeable to the average listener.

#### Pepsiiuk

##### New Member
MikeMI: That’s what I assumed but apparently it’s not.

The perception of sound levels is quite subjective. Most studies indicate that a 3dB change is barely perceptible and a 10dB change causes a doubling of the perceived level.

That is why a 3dB variance in a speaker response with frequency, although appearing to be significant, is not that noticeable to the average listener.
This would make sense with the equation i just found.

SPL = 10log(Power) + sensitivity

Say we have a speaker with 90dB/W/m at 10W

SPL = 10log(10) + 90
SPL = 10 + 90
SPL = 100dB

but with the same speaker at 100W

SPL = 10log(100) + 90
SPL = 20 + 90
SPL = 110dB

which as you said 10dB increase is perceived to be twice as loud.

If this is correct I know where I was going wrong. I assumed that double the perceived volume is a 3dB increase where it is actually a 10dB increase.

Does that mean that a speaker with a sensitivity of 93dB is only slightly loud than one with a sensitivity of 90dB?