Page 52 - The Master Handbook Of Acoustics

27
SOUND LEVELS AND THE DECIBEL

W 1
L 1 =log 10 bels (2-1)
W 2

Because the decibel, from its very name, is ⁄10 bel (from Alexander Gra-
1
ham Bell), the level in decibels of a power ratio becomes:

W 1
L 1 = 10 log 10 decibels (2-2)
W 2

Equation 2-2 applies equally to acoustic power, electric power,
or any other kind of power. A question often arises when levels
other than power need to be expressed in decibels. For example,
acoustic intensity is acoustic power per unit area in a specified
direction, hence Equation 2-2 is appropriate. Acoustic power is
proportional to the square of the acoustic pressure, p, hence the
power level is:

2
p 1
L p = 10 log
2
p 2
p 1
= 20 log in decibels (2-3)
p 2

The tabulation of Table 2-2 will help you decide whether the Equa-
tion 2-2 or Equation 2-3 form applies.

Table 2-2. Use of 10 log and 20 log.

Eq(2-2) Eq(2-3)
a 1
b 1
Parameter 10 log 10 20 log 10
Acoustic a 2 b 2
Power X
Intensity X
Air particle velocity X
Pressure X