38.5 Psychological Effects of Noise

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In this section, certain generally accepted aspects of the psychological effects of noise will be discussed

and quantified. Various indexes have been proposed that quantify the psychological effects of noise.

However, only a few of indices, loudness (sones), noise-criteria (NC) curve, and sound level, are introduced

in the following presentation.

38.5.1 Loudness Interpretation

As was discussed relating to Figure 38.2, loudness level is measured in phons, and the related quantity,

loudness, is measured in sones. A sone is defined as the loudness of a 1000 Hz pure tone with a sound

pressure level of 40 dB. On recalling the definition of loudness level, or by referring to Figure 38.2, one

notes that 40 phon have a loudness equal to 1 sone. This relationship may be simply expressed as

S ¼ 2ðLL 240Þ=10 sone ð38:1Þ

where S ¼ loudness (sones), LL ¼ loudness level (phons), or conversely

LL ¼ 33:2 log S þ 40 phon ð38:2Þ

Example 38.2

Make the following two conversions using the appropriate equation (Equation 38.1 or Equation 38.2):

(1) convert 80 phon to sone, (2) convert 100 sone to phon.

Solution

1. To convert phons to sones, use Equation 38.2:

S ¼ 2ðLL 240Þ=10 ¼ 2ð80240Þ=10 ¼ 24 ¼ 16 sone

2. To convert sones to phons, use Equation 38.2:

LL ¼ 33:2 log S þ 40 ¼ 33:2 log 100 þ 40 ¼ 66:4 þ 40 ¼ 106:4 phon

How should we determine the “total loudness” (sones), when the sound is composed of

multiple frequency components? Probably the most widely used method for establishing the loudness

of a complex noise is that developed by Stevens [2]. The method is based on the measurement of the

1-octave, 1/3-octave, or 1/2-octave band pressure levels. The measured band pressure levels are used

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in conjunction with the equal loudness index contours shown in Figure 38.3 to determine the loudness or

loudness level by means of a simple calculation.

A step-by-step outline of the procedure is as follows:

1. Measure the band pressure levels (1-octave, 1/2-octave, or 1/3-octave) over the frequency range of

interest. Usually, the range chosen is from about 50 to 10,000 Hz.

2. Enter the center frequency and band pressure level for each band in the contour of Figure 38.3, and

determine the loudness index for each band.

3. Calculate the total loudness, St; in sones, by using

St ¼ Imð1 2 KÞ þ K

Xn

i¼1

Ii ðsoneÞ ð38:3Þ

where St ¼ the total loudness (sones), Im ¼ the largest of the loudness indices, Ii ¼ the loudness

indices, including Im, K ¼ weighting factor for the bands chosen. K ¼ 0:3 for 1-octave bands,

K ¼ 0:2 for 1/2-octave bands, K ¼ 0:15 for 1/3-octave bands.

50

10

20

30

40

50

60

70

Band pressure [dB]

80

90

100

110

120

120

100 200 500

Frequency [Hz]

1 k 2 k 5 k 10 k

0.1

0.2

0.3

0.5

0.7

1.0

1.5

2

2.5

3

4

5 6

8

10

12

15

20

30

40

50

60

80

100

150

Loudness

Index

FIGURE 38.3 Equal loudness index contour [2].

Hearing and Psychological Effects 38-5

© 2005 by Taylor & Francis Group, LLC

4. If so desired, one may calculate the loudness level in phons using Equation 38.2, or one may

convert to loudness level by means of the conversion curve of Figure 38.3.

Example 38.3

A particular complex noise was measured to yield the one-octave band pressure given in the

following table

Compute the loudness level using the procedure described before.

Solution

As a first step, the loudness indices are determined from Figure 38.3 and recorded in tabular form with

the band pressure levels. Next, we note that one-octave bands have been used. Therefore K ¼ 0:3 in

Equation 38.3, and

St ¼ Imð1 2 0:3Þ þ 0:3

X8

i¼1

Ii

From the table above, we find that Im ¼ 29.0 sone and, summing up, find

P

Ii ¼ 97:9 sone: Therefore,

St ¼ 29ð1 2 0:3Þ þ 0:3ð97:9Þ ¼ 49:67 sone

We find that the loudness, St ø 50 sone: The loudness level may now be calculated by means of Equation

38.2 as

LL ¼ 33:2 log St þ 40 ¼ 33:2 log 50 þ 40 ¼ 96:4 phon

Therefore, LL; the loudness level, is 96 phon.

38.5.2 Noise-Criteria Curves

Noise-criteria curves, which are neglected here, were established in 1957 for rating indoor noise. The

curves have been utilized as one method of rating background noise level in a room. Each curve specifies

the maximum octave-band sound pressure level for a given NC rating. If the octave band levels for a given

noise spectrum are known, the rating of that noise in terms of the NC curves is given by plotting the noise

spectrum on the set of NC curves to determine the point of highest penetration.

In 1971, some objections to the NC curves led to their modification. The new curves, which are shown

in Figure 38.4, are called the preferred noise-criteria (PNC) curves. Although these curves differ from the

NC curves, they are used in exactly the same manner.

Center Frequency

(Hz)

Band Pressure

Level (dB)

Loudness Index

(sone)

63 66 2.5

125 63 3.2

250 65 4.8

500 70 7.5

1000 73 10.6

2000 76 15.2

4000 81 25.1

8000 79 29.0

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Example 38.4

Solution

The highest penetration is found at 500 Hz on PNC-60. Hence, the answer is PNC-60.

38.5.3 Sound Level

Sound levels are sound pressure levels that have been weighted according to a particular weighting curve.

Three weightings, A, B, and C, and associated sound levels, have been developed as a method to

subjectively evaluate the impact of noise upon the human ear, in a proper manner. The frequency

response and decibel conversions from a flat response for each of these weightings are given in Figure 38.5

and Table 38.1, respectively.

The A-weighting network is now used almost exclusively in measurements that relate directly to the

human response to noise, both from the viewpoint of hearing damage and of annoyance. Such

measurements are referred to as sound level measurements. Sound level is designated by L and the

designated unit is the dBA. Similarly, dBB and dBC are used to designate sound level weighted by B

weighting and C weighting networks, respectively.

31.5

10

20

Octave band pressure level (dB)

30

40

50

60

70

80

63 125 250 500

Octave band center frequencies (Hz)

1000 2000 4000

PNC-15

PNC-20

PNC-25

PNC-30

PNC-35

PNC-40

PNC-45

PNC-50

PNC-55

PNC-60

PNC-65

8000

The approximate

threshold of hearing

for continuous noise

FIGURE 38.4 1971 preferred noise-criteria curves.

Determine the PNC rating for the octave-band noise spectrum tabulated below.

Center frequency (Hz) 63 125 250 500 1000 2000 4000 8000

Band pressure level (dB) 65 60 60 63 55 50 45 40

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FIGURE 38.5 Frequency response for the A, B, and C weighting networks.

TABLE 38.1 Sound Level Conversion Chart from Flat

Response to A Weighting

Frequency (Hz) A Weighting (dB)

50 2 30.2

63 2 26.2

80 2 22.5

100 2 19.1

125 2 16.1

160 2 13.4

200 2 10.9

250 2 8.6

315 2 6.6

400 2 4.8

500 2 3.2

630 2 1.9

800 2 0.8

1,000 0

1,250 þ0.6

1,600 þ1.0

2,000 þ1.2

2,500 þ1.3

3,150 þ1.2

4,000 þ1.0

5,000 þ0.5

6,300 2 0.1

8,000 2 1.1

10,000 2 2.5

12,500 2 4.3

16,000 2 6.6

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In noise-abatement problems, it is often necessary to convert calculated a 1-octave-band or 1/3-

octave-band sound pressure level to a total sound level in dBA. Table 38.1 gives sound level conversion by

A weighting from flat response pressure.

Example 38.5

Determine the total A weight sound level, L; of the set of octave-band sound pressure levels given in

Table 38.2.

Solution

Refer Table 38.1 for the dB conversion from a flat response level, Lflat; for each of the octave bands to a

sound pressure intensity with A weighting IiA; and then the sum of IiA: Finally, the total sound level with

A weighting Ltotal;A is given by

Ltotal;A ¼ 10 log

Xn

i¼1

IiA ¼ 10 log 12:238 £ 106 ¼ 70:9 ðdBÞ

References

1. Irwin, J.D. and Graf, E.R. 1979. Industrial Noise and Vibration Control, Prentice Hall, Englewood

Cliffs, NJ.

2. American National Standard USAS S3.4-1968. 1968. Procedure for the Computation of Loudness of

Noise, America National Standards Institute, New York, NY.

TABLE 38.2 Octave-Band Sound Pressure Levels

fc (Hz) Lflat (dB) DLA (dB) LA ¼ Lflat þ DL (dB) IiA

63 74 2 26.2 47.8 0.60 £ 105

125 71 2 16.1 54.9 3.09

250 61 2 8.6 52.4 1.74

500 60 2 3.2 56.8 6.31

1000 62 0 62.0 1.585 £ 106

2000 60 1.2 61.2 1.318

4000 62 1.0 63.0 1.995

8000 69 2 1.1 67.9 6.166

Sum 12.238 £ 106

Note:

* fc: band center frequency

* Lflat: sound pressure level with flat weighting

* DLA: A-weighting level

* IiA: sound pressure intensity with A weighting.

Hearing and Psychological Effects 38-9

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