In the field of audio, “dB” is frequently encountered, and frequently misunderstood. Among the most common questions are:
- Why does Audacity / (any other audio editor) show “dB” as negative while dB meters show positive values?
- Is “dB” a measure of loudness?
- How many Volts is 1 dB?
- What are; dB FS, dBA, dB SPL, dB RMS, …
- …
A common misconception is that “dB” is a “unit of measurement” (like grammes, meters, seconds, volts, …), but that is incorrect. “dB” is a ratio. It is a measure of how much bigger or smaller one thing is compared to another. Positive dB means bigger, while negative dB means smaller.
In the case of Audacity, and more generally anything that is dealing with signal levels, “dB” is a measure of how much smaller the signal is compared with full scale (the full track height). This is also known as “dBFS” (dB relative to full scale). Because signals are nearly always less than full scale, the dB value is usually negative.
In the case of “Sound pressure levels” (db SPL), it is a measure of how much bigger the sound is compared to “20 micro pascals”, which is a very very quiet sound (around the limit of human hearing). Because sounds of interest are nearly always bigger than 20 micro pascals, SPL measurements are usually positive.
What does “dB” stand for?
“dB” is an abbreviation of “decibel“, which is one tenth of a “bel“, which was named after the Scottish inventor Alexander Graham Bell. Because a “bel” is so big, it is rarely used
How much is a decibel?
When referring to measurements of power quantities, a decibel is defined as ten times the base-10 logarithm of the ratio of the measured quantity to reference value. This may be written as:
10*log(P/P0)
where “P” is the power of the thing being measured, and P0 is the reference level.
When referring to measurements of amplitude quantities, a decibel is defined as twenty times the base-10 logarithm of the ratio of the measured quantity to reference value. This may be written as:
20*log(A/A0)
where “A” is the amplitude of the thing being measured, and A0 is the reference amplitude.
Audio signal example
If you have a signal (waveform) in an Audacity track that is half the height of the track, then the reference level (“full scale”) is the full height of the track. Thus we can say that the reference amplitude is 1, and the amplitude of the signal is 0.5. Reaching for a calculator we can quickly see that;
20*log(0.5) = -6.020599913 dB
Rule of thumb
As seen above, half of full scale is very close to -6 dB. Similarly, because dB is a ratio, we can say that double full scale would be +6dB. The general rule of thumb is that doubling the amplitude is an increase of 6 dB, and a halving of amplitude is a decrease of -6dB.
- Full track height = 0 dB
- Half track height = -6 dB
- Quarter track height = -12 dB
- Eighth track height = 18 dB
- Sixteenth track height = -24 dB
- and so on.
Further reading:
See also this Wikipedia page: https://en.wikipedia.org/wiki/Decibel