2.10 WEIGHTED SOUND LEVELS

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Most sound level meters have three ‘‘weighting’’ networks, called the A-, B-,

and C-scales (ANSI S1.4, 1971). Originally, the A-scale was designed to

correspond to the response of the human ear for a sound pressure level of

40 dB at all frequencies. The B-scale was designed to correspond to the

response of the human ear for a sound pressure level of 70 dB at all frequencies.

The C-scale was approximately flat (constant) for frequencies

between 63 Hz and 4000 Hz.

The B-scale is rarely used at present. The A-scale is widely used as a

single measure of possible hearing damage, annoyance caused by noise, and

34 Chapter 2

TABLE 2-3 Standard Octave Bands

Band No.

Frequency, Hz

Lower, f1 Center, f0 Upper, f2

12 11 16 22

15 22 31.5 44

18 44 63 88

21 88 125 177

24 177 250 355

27 355 500 710

30 710 1,000 1,420

33 1,420 2,000 2,840

36 2,840 4,000 5,680

39 5,680 8,000 11,360

42 11,360 16,000 22,720

Source: ANSI S1.6 (1967).

Copyright © 2003 Marcel Dekker, Inc.

compliance with various noise regulations. The sound levels indicated by the

A-scale network are denoted by LA, and the units are designated dBA.

The weighting for the A- and C-scale is shown in Table 2-4. These

values are also plotted in Fig. 2-6. The large negative weighting factor for

low-frequency sounds corresponds to the fact that the human ear is not as

sensitive to low-frequency sound as it is for sound at frequencies in the

1 kHz to 4 kHz range. For example, a sound having a sound pressure

level of 40 dB at 63 Hz would be perceived by the human ear as having a

sound pressure level of approximately р40 _ 26Ю ј 14 dB. Alternatively,

a sound that was perceived to have a sound pressure level of 40 dB for

a frequency of 63 Hz would actually have a sound pressure level of

р40 ю 26Ю ј 66 dB. Because the human ear does not respond as significantly

to low-frequency sounds, noise at low frequencies (63 Hz, for example) is

generally not as damaging or annoying as sound at high frequencies (2 kHz,

for example).

If the sound pressure level spectrum is measured or calculated for each

octave band, the A-weighted sound level may be calculated, using the Aweighting

factors (CFA) from Table 2-4:

LA ј 10 log10Ѕ_10рLpюCFAЮ=10_ (2-45)

where the summation is carried out for all octave bands. The A-scale conversion

process is illustrated in the following example.

Example 2-7. The measured octave band sound pressure levels around a

punch press are given in Table 2-5. Determine the A-weighted sound level

and the overall sound pressure level.

Basics of Acoustics 35

TABLE 2-4 Weighting Factors for the A- and C-Scales

Octave band center frequency, Hz A-scale CFA C-scale CFC

31.5 _39:4 _3:0

63 _26:2 _0:8

125 _16:1 _0:2

250 _8:9 0:0

500 _3:2 0:0

1,000 0:0 0:0

2,000 ю1:2 _0:2

4,000 ю1:0 _0:8

8,000 _1:1 _3:0

16,000 _6:6 _8:5

Source: ANSI S1.4 (1971).

Copyright © 2003 Marcel Dekker, Inc.

The sound levels with the weighting factor applied are given in Table

2-5. The A-weighted sound level is calculated from Eq. (2-45).

LA ј 10 log10Ѕ1030:6=10 ю 1054:8=10 ю 1072:9=10 ю_ _ __

LA ј 10 log10р1:3532 _ 1010Ю ј 101:3 dBA

The overall sound pressure level is obtained by adding the individual

unweighted octave band sound pressure levels given in Table 2-5, using

‘‘decibel addition’’, Eq. (2-43):

36 Chapter 2

FIGURE 2-6 Weighting factors for the A- and C-scales. CFA ј conversion factor to

A-scale; CFC ј conversion factor to C-scale.

TABLE 2-5 Data for Example 2-7

Octave band center frequency, Hz

31.5 63 125 250 500 1,000 2,000 4,000 8,000

Lp(OB), dB 70 81 89 101 103 93 83 77 74

CFA, dB _39:4 _26:2 _16:1 _8:9 _3:2 0.0 ю1:2 ю1:0 _1:1

Lp

ю CFA, dB 30:6 54:8 72:9 9:1 99.8 93.0 84.2 78.0 72.9

Copyright © 2003 Marcel Dekker, Inc.

Lp ј 10 log10Ѕ_10Lp=10_

Lp ј 10 log10Ѕ1070=10 ю 1081=10 ю 1089=10 ю_ _ __ ј 10 log10р3:5742 _ 1010Ю

Lp ј 105:5dB

We note that the A-weighted sound level is lower than the overall

sound pressure level in this problem. The reason for this difference is that

the sound energy is more predominant in the lower octave bands, such as

the 250 Hz band. The readings are diminished in the lower frequencies

(compare Lp and Lp ю CFAЮ when the A-weighting is applied. The Aweighted

sound level can be larger than the overall sound pressure level if

the sound energy is more concentrated in the octave bands between 1 and

4 kHz.

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