Audio Engineering

28 Chapter 1

 























     

Figure 1.22 : (a) The logarithm of a number is the power to which the base (in this case 10)

must be raised to obtain the number. (b) Multiplication is obtained by adding logs, division

by subtracting. (c) The slide rule has two logarithmic scales whose length can be added or

subtracted easily.

Figure 1.23 : (a) The Bel is the log of the ratio between two powers, that between two

powers, that to be measured, and the reference. The Bel is too large so the decibel is used

in practice. (b) As the decibel is defi ned as a power ratio, voltage ratios have to be squared.

This is done conveniently by doubling the logs so that the ratio is now multiplied by 20.

1 Bel  log 10 PP^1

2

P 1

P 2

1 decibel  1/10 Bel

Power ratio (dB)  10 log 10

(a)

As power V^2 , when using voltages:

Power ratio (dB)  10 log V

(^21)
V^22
V 1
V 2
 10 log 2
V 1
V 2
 20 log
(b)