Decibels tell you how much louder a sound is than some reference level of sound pressure. The reference that is nearly always used is a pressure of 20 micropascal, which is considered to be the threshold of human hearing. So 0 dB is the point at which a sound is exactly as loud as this value, meaning you might just about be able to hear it. Anything below 0 dB you most likely won’t be able to hear at all.
The way decibels work is that they are on a log scale. You start with a ratio: the ratio of your measurement to the reference level. For instance, if we take 20 micropascal as the reference, then a sound pressure of 2 millipascal is 100 times louder than that. To convert this to decibels, we calculate the logarithm of 100 in base-10, and then multiply this by 10. The base-10 log of 100 is 2 (10^(2)=100), and so a sound pressure of 2 millipascal corresponds to 2*10=20 dB.
In other words, every 10 dB increase means the sound gets 10 times louder. Every 3 dB corresponds (approximately) to a doubling of the loudness.
If our measurement is equal to the reference, i.e. also 20 micropascal, then the ratio between them is 1, and the logarithm of 1 (in any base) is 0, which is how we get to 0 dB.
How about negative decibel values? Well, they arise when your measured sound is *quieter* than your reference. For instance, a sound pressure of 0.02 micropascal is 1000 times quieter than our standard reference, and so that corresponds to -30 dB. In the case of a -23 decibel room, that corresponds to a sound pressure that is 10^(2.3) ≈ 200 times quieter than the threshold of human hearing. The way you measure that is obviously not using human ears, but with a more sensitive sound level meter.
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