1 Decibel Mathematics

The standard for representing power ratios is the bel (B). If we increase an initial power value by a factor of 10, we say that it has increased by 1 bel. If we increase the power by a factor of 100 (= 10 · 10, or 102), we say that it has increased by 2 bels. Increasing the power by a factor of 1,000 (= 10 · 10 · 10, or 103) would be an increase of 3 bels, and so forth.

As you can see, even with small increases in bels, the power ratios quickly become very large. For example, increasing by 6 bels is the same as increasing by a factor of 1 million! To avoid having to work in fractions of bels, we use the more common decibel (dB) system. 10 decibels equals 1 bel.

1 dB also conveniently corresponds to roughly the ...

Get Audio Production Tips now with the O’Reilly learning platform.

O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.