a Power vs Volume Question

This is a simplified response:

Sound pressure levels are expressed in dB and the softest sound a normal person can hear is around 4dB. The threshold of pain is somewhere around 130dB, but this isn't 32.5 times the pressure level of 4dB. It is closer to 4,000,000,000,000 times the pressure level since the scale is logarithmic.

130db – 4dB = 126dB
126dB = 10 times log (pressure at 130dB divided by pressure at 4dB)
12.6 = log (pressure at 130dB divided by pressure at 4dB)
Inverse log 12.6 = about 4,000,000,000,000

This isn't exactly the same thing as loudness since it takes about 10 times the pressure level (10db) to be perceived as twice as loud and the ear's sensitivity changes with frequency and pressure level, but they are correlated.

check this out

loudness

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Pawlowski, the decibel is a logarithmic function, not a linear one. Each doubling of power increases loudness by 6 db. The ear perceives a 10 db increase in sound level as a doubling of volume.

A jet plane taking off is around 130 db. A rocket launch close hand is around 180 db.

Each doubling of power increases loudness by 6 db. The ear perceives a 10 db increase in sound level as a doubling of volume.

Actually a doubling of power is 3dB, a doubling of voltage is 6dB.

Loudness and volume are the same thing.

It should read "Each doubling of power increases sound pressure levels (SPL) by 3 db. The ear perceives a 10 db increase in SPL as a doubling of volume."

Further to Herman above, each doubling of SOUND PRESSURE level (i.e. spl), i.e. what we "listen to", is 6dB. You need four times the "power" to achieve double sound pressure -- in fact twice "as loud". Yr mic should record +6 dB when your power rises 4times.
In other words... on paper, going from 200W to 300W gives you an extra 1,4dB. That's assuming, of course, that the speakers can take 300W continuous -- which they usually can't.

Twice the power is a 3db increase.
10db is twice the volume or loudness.