If in Digital Sound Software there’s a meter from -60 to 0, what’s the best “range” (for the lack of knowledge) of sound someone can record at? Considering that people who will listen to that recording can adjust their speaker volumes up and down.
In: Engineering
First of all, what we perceive as sound are air vibrations, meaning diferences of air pressure reaching our eardrums and making moving it. Mark this!
dB is a relative logarithmic scale. Let’s go by parts! First it is a relative scale, meaning there is a reference sound used as the fractional base. Let’s say there is some reference sound with “power” (that will be defined afterwards) p0. We can measure all sounds as how much they are more powerful or less power full than p0 using fractions. For example, let’s say there is a sound 10 times as powerful as p0, we can say the power p of the sound is:
p= 10 x p0
Or:
p/p0 = 10
So, if we have a known reference sound, we can always explain how loud another sound is as a multiple of the referente sound. In this case the sound is 10 times the reference sound. This would be perfect if we where talking about linear things, but a lot of thing are not. When we talk about sounds in specific,the pressure difference in air is the most physically meaningful thing to talk about, but if we take a sound wave with the double of the air pressure difference it will not sound 2 times louder to us. Actually the loudness we fell in sound follows a logarithmic scale. Meaning, if we take a sound and make the difference of pressure 10 times greater, we will feel it as twice as loud. If we we take a sound with 100 times the difference in pressure, we will feel as trice as loud. There is a mathematical function that perfectly reproduces this. It’s the log function. The log function tells us what power we must use to the make a number reach it’s argument. For example:
log10(10) = 1, because 10^1 = 10
log10(100) = 2, because 10^2 = 100
We could use any base number, but the Bell scale usually uses the base 10. So, if we take a reference sound with pressure difference p0, and another sound with diference of pressure p, the power of the sound p in the Bell scale would be:
B = log10(p/p0)
But the Bell scale can be to large to be useful, so we divide the Bell scale by ten, building the deciBell scale (deci means a “tenth of”):
dB = log10(p/p0)/10
This is the meaning of the dB scale. Negative values means that the sound power you measured is lesser than the reference sound. For example, let’s say you measured a sound 10 times quieter than the reference sound (p = p0/10). The equation above would be:
dB = log10(p0/(10*p0)/10 = log10(1/10)/10 = -1/10 = -0.1
Notice that the dB scale is zero when the measured sound is as loud as the reference sound, positive when is louder and negative when is quieter.
Now, you may ask what is the reference sound for the dB scale. Well, it’s complicated and I think it is outside the scope of the question! But I’ll give a fast explanation. The Bell and the deciBells scales have their name because they created in the Bell Labs as a measure of signal power in telegraphs lines. As an electric signal is propagated through a wire, some of its power is lost due to electric resistance that converts part of the electric energy into heat. When telephones where invented, the dB was used as a measure of how much loudness reached a far telephone compared to the loudness of a person speaking. But loudness is related with sound wave’s energy and it depends on its frequency. So dB scale also depends on the sound frequencies!
Nowadays we consider that p0 is the power of a sound wave with 1 microPascal RMS of pressure diference in water, or 20 microPascal RMS of pressure diference in the air. RMS is another complication that is also out of scope, so I’ll omit unless you want a more in depth explanation!
But, in specific, sound recorder softwares, go from negative to zero, because it considers the maximum loudness it can capture as reference. Meaning, negative infinity is absolute silence and zero is the loudest sound it can capture. So, if you want a good range of quietness and loudness and/or no distortion, you should never reach zero in any sound frequency. If you do, the wave form will be “clipped”, so louder sounds will sound “square”, rough, distorted.
One good reference: [https://en.wikipedia.org/wiki/Decibel](https://en.wikipedia.org/wiki/Decibel)
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