Audio Engineering

36 Chapter 2

For example, if a 2:1 change is equivalent to 3.01 dB, then

log multiplier

Base





log.

log

()301

2

10 (2.6)

o r

10 log 2  3.01.

M logbac NM

a

cb

NM

()M

10 log 10 2  3.01 dB

3.01

2  10 (^10 )

Logarithmic Form

Exponential Form

Figure 2.2 : Conversion of dB from logarithmic form to exponential form.

Table 2.1 : Power Ratios in Decibels

Power ratio Decibels (dB)

2 3.01030

3 4.77121

4 6.02060

5 6.98970

6 7.78151

7 8.45098

8 9.03090

9 9.54243

10 10.00000

100 20.00000

1000 30.00000

10,000 40.00000

100,000 50.00000

1,000,000 60.00000