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Sound volume is often measured in decibels. The decibel scale works in mnany ways. LOL

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Many ways indeed! it's not a simple matter, and we have to distinguish between intensity and power, which are not the same things. Most sound volumes figures are of Sound Pressure Level (SPL) in deciBels, and this is a brief explanation. It helps if know basic logarithm principles!

The deciBel (dB) is not a measure of power or intensity of sound only, but can describe any acoustic, electrical or electromagnetic signal, so to use it properly you have to specify the right units and scale.

Further, it is not a linear unit like a metre or a litre, but a product of a constant with the logarithm of a ratio! And that ratio's denominator is the reference levelrelevant to what you are measuring, and to which you compare the measured level.

We use this logarithmic scale because the human ear is roughly logarithmic in response to sound pressure; and the maximum pressure it can bear for a short time painfully but without injury is 1 million times the faintest it could hear before too many of those maxima hit it for too long.

In measuring sound in air by deciBels, you use 20µPa (20 micro-Pascals), where the Pascal is the official SI unit of pressure. It's an extremely tiny pressure, but still too big for acoustics, where you need to work in millionths of Pascals - i.e. micro-Pascals. (The standard abbreviation for 'micro' is the Greek letter µ.)

Why 20µPa? It is the SPL of the faintest sound the fully-healthy human ear can detect - a staggeringly low 1/(5000 000 000) of Standard Atmospheric Pressure.

So deciBels avoid clumsy calculations with lots of big exponents, and turns many of the sums into just adding and subtracting modest numbers.

Therefore, measuring sound level in air, and without going into the derivation of the 20 constant, the SPL = [ 20 log-base-10 (measured pressure µPa / 20µPa) ] deciBels.

So to quote the sound pressure level fully, it is N dB re[ferred to] 20µPa.

Marine acoustics - dolphin calls, sonar etc. - uses a mere 1µPa as reference, so the two sound scales are not readily comparable.

A measured level equal to its reference is 0dB in whatever scale you use, because the ratio is then 1, and as log-base-10(1) = 0, so 20log(1) = 0.

Why can't you count from 0µPa? Because that makes the denominator 0, and you can't divide by 0.

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