Handbook for Sound Engineers

24 Chapter 2

Fig. 2-2. The decibel scale is more resolute than the Bel
scale.

The decibel is always a power-related ratio. Elec-
trical and acoustical power changes can be converted
exactly in the manner described. Quantities that are not
powers must be made proportional to power—a rela-
tionship established by the power equation.

(2-1)

where,
W is power in watts,

E is voltage in volts,
R is resistance in ohms.

This requires voltage, distance, and pressure to be
squared prior to taking the ratio. Some practitioners

prefer to omit the squaring of the initial quantities and

simply change the log multiplier from ten to twenty.

This produces the same end result.

Fig. 2-3 provides a list of some dB changes along

with the ratio of voltage, pressure, distance, and power

required to produce the indicated dB change. It is a

worthwhile endeavor to memorize the changes indicated

in bold type and be able to recognize them by listening.

A decibel conversion requires two quantities that are

in the same unit, i.e., watts, volts, meters, feet. The unit

cancels during the initial division process, leaving the

ratio between the two quantities. For this reason, the

decibel is without dimension and is therefore techni-

cally not a unit in the classical sense. If two arbitrary

quantities of the same unit are compared, the result is a

relative level change. If a standard reference quantity is

used in the denominator of the ratio, the result is an

absolute level and the unit is dB relative to the original

Figure 2-1. A logarithmic scale has its increments marked by a fixed ratio, in this case 10 to 1, forming a more compact
representation than a linear scale. Courtesy Syn-Aud-Con.

Figure 2-2. The steps to performing a decibel conversion are outlined. Courtesy Syn-Aud-Con.

0 1 k 10 k 20 k 30 k 40 k 50 k

1 10 100 1 K 10 K 100 K

Linear scale

Log scale

W E

2

R

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