Guidelines on noise control
Guidelines for
Noise Control & Vibration
Reproduced Dec 2003
© MINISTRY OF MANPOWER, SINGAPORE, 2003 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanized, photocopying, recording or otherwise, without the prior permission of the copyright holder.
Occupational Safety and Health Division Ministry Of Manpower 18 Havelock Road #03-02 Singapore 059764
Contents
Page
Preface
1
Fundamentals of Sound and Terminology
2
Legal Requirements on Noise Control
13
Cost Benefit Analysis of Noise Control
15
Noise Exposure Limits and Criteria
17
Priority and Methods of Control
22
Plant Planning
27
Engineering Noise Control Materials
34
Noise Barriers
42
Partition Walls
48
Machine Enclosures
54
Personnel Enclosures
64
Room Absorption
66
Damping
70
Noise Control from Material Handling and Vibrating Surfaces
74
Vibration Control
77
Silencers or Mufflers
91
Active Noise Control
102
Preface Noise is one of the prevalent health hazards in industry. Exposure to excessive noise can cause noise-induced deafness or hearing loss - a disease that may take several years to develop and cannot be cured. Fortunately, noise hazard can be controlled. No matter what the noise problems may be in a particular workplace, methods and measures exist to reduce or control the hazard. Noise-induced deafness can therefore be prevented and should be prevented. The main purpose of the guidelines is to provide technical information on how industrial noise can be controlled by engineering means such as the use of barriers, enclosures, partition walls, sound absorbers, damping materials, silencers and isolators. Modification or substitution of noisy processes or equipment and application of innovative technology such as active noise control may also be the solutions to noise control. The first edition of the Guidelines was published in 1985. The second edition was produced in 1999. It was used as one of the main sources of reference in the preparation of the Singapore Standards Code of Practice for Industrial Noise Control. This latest edition updates and refines the guidelines. New sections are added, these include legal requirements on noise control, noise sources identification, cost-benefit of noise control, and specific machinery noise and vibration control. In addition, many diagrams and photos on noise and vibration control are incorporated to showcase engineering controls. The guidelines should help plant engineers, acoustics specialists or service providers, safety and health professionals, technical personnel and people working in the industry who have little knowledge of acoustics but who want to develop a practical approach to controlling noise and vibration problems occurring in the workplaces.
1
1
FUNDAMENTALS OF SOUND AND TERMINOLOGY Sound is generated by vibration of surface or by turbulent fluid flow, which sets the air molecules into motion. It is a wave motion due to air pressure variations. Sound can propagate in gases, liquids and solids, but it cannot propagate in a vacuum. Noise carries the meaning of unwanted sound but the two terms are often used interchangeably. Propagation of Noise When a noise source is placed in an outdoor environment, the sound waves will propagate from the source and there are no boundaries present to reflect the sound waves. However, when it is located within a room or building, the sound waves will be reflected from the boundaries of the room or building. The noise levels which a worker can be subjected to, is influenced by three factors: (1)
The direct field noise from his machinery, or one very near him.
(2)
The reflected or reverberant field noise from one or more machines further away from him.
(3)
The combination of the direct field noise of the nearest machine and reverberant field noise of other machines.
Reflected sound Noise source Direct sound
Fig 1 Propagation of noise in a room
2
Sound Frequency The frequency of sound wave is the rate at which the air pressure variations occur. Frequency is perceived as the pitch of a sound and is expressed in cycles per second (c/s) or Hertz (Hz). Even though sound may consists of a single pure tone, in most cases, it consists of many tones of different frequencies and intensities. Frequency Band (Octave Band and 1/3 – Octave Band) In noise and vibration control, the spectrum of the noise and the vibrations are normally divided into some frequency bands, and each frequency band has an upper frequency limit, a lower frequency limit and a centre frequency. An octave band is a frequency bandwidth that has an upper band-edge frequency equal to twice its lower band-edge frequency. The octave band is the most common frequency bandwidth used for industrial noise control measurements. The standard range of octave bands has the following centre frequencies: 31.5, 63, 125, 250, 500, 1,000, 2,000, 4,000, 8,000 and 16,000 Hz. The standard range of 1/3 – octave bands has the following centre frequencies: 31.5, 40, 50, 63, 80, 100, 125, 160, 200, 250, 315, 400, 500, 630, 800, 1,000, 1,250, 1,600, 2,000, 2,500, 3,150, 4,000, 5,000, 6,300, 8,000, 10,000, 12,500 and 16,000 Hz. Wavelength The wavelength of a sound wave is the distance the wave travels during one cycle. Wavelength is related to frequency by:
λ=
c f
(1)
where λ is the wavelength, m c is the speed of sound, m/s f is the frequency, Hz Low frequency sound has a long wavelength whereas high frequency sound has a short wavelength. Speed of Sound in Air The speed of sound in air is the speed at which the sound waves propagate. It is dependent on temperature and can be calculated by:
3
c = 20 × 273 + T
(2)
where c is the sound speed, m/s T is the temperature, oC The speed of sound in air at room temperature (25 oC) is approximately 345 m/s. Free Field A free field is a region of space where sound waves can propagate without any obstruction. In a free field, sound pressure levels attenuate in accordance with the inverse square law, or with 6 dB attenuation for each doubling of the distance from a point source. Near Field Near field is defined as a region very near a noise source. The near field usually occurs at a distance less than one wavelength from the vibrating surface of the source. In this region, the sound pressure levels do not decrease by 6 dB each time the distance from the source is doubled. Far Field Further away from the source, there is a far field in which the source can be treated as a point source at which the sound pressure levels fall off at a rate of approximately 6 dB per doubling of distance. Direct Field The direct field of a sound source is defined as that part of the sound field, which has not suffered any reflection from any room surfaces or obstacles. In the direct field, the sound level is dominated by the sound directly radiated from the source, and is independent of the room acoustics. Any control of the sound level must be by the direct reduction of the energy or power of the source. Diffused Field Diffused field is a sound field where the sound energy density is nearly uniform throughout the sound field.
Reverberant Field 4
The reverberant field is defined as the area where the reflected sound has a dominant effect on the sound levels. The far field can lead, but not always, into the reverberant field, which fills the rest of the room space. The reverberant field is usually uniform within the room except in the region of the source or near highly absorbing areas. The sound level in the reverberant field is controlled by the power of the source, the size of the room, and the amount of sound absorbing material within the room. Sound Power Level The sound power of a source is the amount of acoustic energy being generated per unit time by the source. The sound power level is defined as: LW = 10 log
W WO
(3)
where LW is the sound power level, dB W is the sound power, watts (W) -12 Wo is the reference sound power of 10 W It should be noted that LW is a constant for a particular source, and is independent of the distance or acoustic environment. Sound Intensity Level Sound intensity is the amount of sound power passing through a unit surface area. The sound intensity level is defined as: LI = 10 log
I IO
(4)
where LI is the sound intensity level, dB I is the sound intensity, W/m2 Io is the reference sound intensity of 10-12 W/m2 Sound Pressure Level Sound pressure refers to the root mean square value of the pressure changes over and below the atmospheric pressure. The sound pressure level is defined as:
5
2
P = 20 log P L P = 10 log P P ref ref where LP is the sound pressure level, dB. P is the sound pressure, pascals (Pa) Pref is the reference pressure, 2 x 10-5 Pa
(5)
The reference pressure is the pressure of the threshold of hearing. LP is dependent on the distance from the source, and the absorption characteristics of the environment “A” Weighting Sound Pressure Level The “A” weighting scale is used to correct the direct noise levels to the levels heard by the ear. This corrected noise level is called dBA and is commonly used in noise measurement. To obtain the dBA levels from the octave band data, the correction factors below must be applied: Table 1 “A” weighting factors Octave Band Centre Frequency (Hz)
31.5
Correction Factor
-39.5 -26.2 -16.2 -8.7
63
125
250
500 -3.3
1K 0
2K
4K
8K
16K
+1.2
+1.0
-1.1
-6.6
Addition of Noise Levels A frequent calculation in noise control engineering involves the addition of noise levels. The formula for calculating the total or combined effect of two or more sound pressure levels is: Li 10
n
LT = 10 log[∑10 ]
(6)
i
where LT is the total sound pressure level, dB or dBA Li is the individual sound pressure level, dB or dBA Example Three machines produce noise levels of 86 dB, 84 dB and 89 dB when operated individually. What is the combined noise level if all the three machines operate simultaneously? The combined noise level is:
6
86
84
89
LT = 10 log[10 10 + 10 10 + 10 10 ] = 10 log[108.6 + 10 8.4 + 10 8.9 ] = 91.6 dB The table below can be used to combine sound levels without using the formula: Table 2 Adding sound pressure levels Difference in noise level
Amount to be added to the higher level
0 1 2 3 4 5 6 7 8 9 10
3.0 2.5 2.1 1.8 1.5 1.2 1.0 0.8 0.6 0.5 0.4
Example If two independent noises with levels of 83 and 87 dB are produced at the same time at a given point, the combined noise level will be 87 + 1.5 = 88.5 dB, since the amount to be added to the higher level, for a difference of 4 dB between the two levels, is 1.5 dB. Subtraction of Noise Levels Sometimes it may be necessary to subtract one noise level from another, for example, when background noise must be subtracted from combined noise to obtain the sound produced by the machine alone. The method used is similar to that described in the addition of noise. Example The noise level measured at a particular location in a factory with a noisy machine operating nearby is 92 dBA. When the machine is turned off, the noise level measured is 88 dBA. What is the level due to the machine alone?
7
Machine noise is: 92 10
88 10
LT = 10 log[10 − 10 ] = 10 log[109.2 − 108.8 ] = 89.8 dB For noise-testing purposes, this procedure should be used only when the total noise exceeds the background noise by 3 dB or more. If the difference is less than 3 dB, a valid sound test probably cannot be made. Combining Octave Band Levels The above method can also be used to combine individual octave band readings to obtain the overall noise level. The appropriate “A” weighting factors (Table 1) are first applied to each octave band sound level and the A-weighted sound level are then combined using the above method. Example If the following octave band readings are predicted in a design calculation, the overall noise level can be estimated as follows: Frequency (Hz)
Sound level (dB)
“A” weighting factor
A-weighted level (dBA)
31.5 63 125 250 500 1K 2K 4K 8K 16K
74 66 71 61 60 75 82 80 87 90
-39.5 -26.2 -16.2 - 8.7 - 3.3 0 + 1.2 + 1.0 - 1.1 - 6.6
34.5 39.8 54.8 52.3 56.7 75.0 83.2 81.0 85.9 83.4
n
Li 10
LT = 10 log[∑10 ] i
= 10 log[10 = 90 dBA
34.5 10
39.8
54.8
52.3
56.7
75
83.2
81
85.9
83.4
+ 10 10 + 10 10 + 10 10 + 10 10 + 10 10 + 10 10 + 10 10 + 10 10 + 10 10 ]
8
Directivity Factor The directivity factor, Q is a measure of the degree to which sound is concentrated in a certain direction rather than radiated evenly in a full spherical pattern. It is defined as: Q=
Iθ Is
(7)
Where Iθ is the sound intensity at some distance from the source and at an angle θ to a specified axis of a directional noise source Is is the sound intensity produced at the same distance from a uniformly radiating sound source of equal sound power For free field radiation, that is, where there are no reflections of sound, Q = 1. For hemispherical radiation of sound, such as in areas where the sound source is on the floor of a room or at ground level in the outdoors, such that ½ spherical radiation exists, Q = 2. If the sound source is near the intersection of the floor and a wall of a room such that ¼ spherical radiation exists, Q would be 4. If the sound source is near the intersection of the floor and two walls such that 1/8 spherical radiation exists, Q would equal 8.
Q=1
Q=8
Q=4 Q=2
Fig 2 Directivity factor of noise source at different locations in a room Sometimes the sound source itself might have a directional radiation pattern. If so, this would have to be taken into account in addition to the environmental radiation pattern discussed above. Room Constant The room constant is a measure of the ability of a room to absorb sound. It can be calculated by the following equation:
9
_
R=
αS
(8)
_
1−α 2 where R is the room constant, m sabins S is the total surface area of the room, m
2
_
α is the average absorption coefficient of the room surface. _
α can be calculated as follows: _
α=
α 1 S1 + α 2 S 2 + .... + α n S n S1 + S 2 + .... + S n
α i Si i =1 S i n
=∑
(9) 2
where Si is the area of each absorbing surface, m α i is the corresponding absorption coefficient of the surface Example Calculate the average absorption coefficient and the room constant, at 1000 Hz of a room 15 m long, 10 m wide and 4 m high; The floor is painted concrete, the ceiling is smooth finish plaster, and the walls are of wood panelling.
Floor Ceiling Side walls End walls Total:
_
α = =
∑α
i
Surface area 2 Si (m )
Absorption coefficient, αi
α i Si
15x10 15x10 (15x4) x 2 (10x4) x 2 -----------500 =======
0.07 0.03 0.09 0.09
10.5 4.5 10.8 7.2 ------33 ====
Si
S 15 * 10 * 0.07 + 15 * 10 * 0.03 + 15 * 4 * 2 * 0.09 + 10 * 4 * 2 * 0.09 500
= 0.66 _
R =
α S _
1−α
=
0 . 066 × 500 1 − 0 . 066
= 35 m2 sabins
10
Reverberation Time and Room Absorption The term “αS” in equation (8) is known as room absorption “A”. Room absorption is related to the decay rate of reflected sound which is commonly measured in terms of reverberation time, T60. T60 = 0.161 V / A
(10) 3
where V is the room volume in m . Reverberation time is defined, as the time required for the average sound pressure level to decay 60 dB, or in terms of sound pressure, to 1/1000th of its original value after the sound source has been shut off. In practice, reverberation time can be measured by noting the time required for an impulsive sound to decay 60 dB from its original or peak value. Example 3 The reverberation time in a 12 m x 10 m x 3 m or 360 m room is 1.7 s, the room absorption is: A = 0.161 x 360/1.7 = 34 metric sabins The total surface area of the room is {(12x10) + (12x3) + (10x3)} x 2 2 = 372 m , its average absorption coefficient is: _
α = 34/372 = 0.09 Relationship between Sound Pressure Level and Sound Power Level Many industrial noise problems are complicated by the fact that the noise is confined in a room. Reflections from the wall, floor, ceiling and equipment in the room change the sound wave characteristics from those for free field radiation. The relationship between the sound pressure level and the sound power level is: 4 Q + ] LP = LW + 10 log[ 2 (11) R 4πr where LP is the sound pressure level, dB LW is the sound power level, dB Q is the directivity factor of the sound source 2 R is the room constant, m sabins r is the distance in m from the source to the point where LP is determined 11
Fig. 3 can be used as a quick guide to determine if sound absorption treatment reduces the noise level at a given location.
Figure 3 Relative sound pressure levels versus distance from the source Example Suppose a new machine is placed on the floor of a room. The room has a 2 total surface area of 200 m and the average absorption coefficient is 0.2. A sound power level of the machine is 94 dB. The directivity factor Q = 2, and 2 the room constant R = (0.2 x 200)/(1-0.2) or 50 m sabins. The sound pressure level is:
Q 4 + ] 2 R 4πr 2 4 94 = Lp − 10 log[ + ] 2 4π 2 50
LW = LP − 10 log[
Lp = 85 dB
12
Noise Control & Vibration
Reproduced Dec 2003
© MINISTRY OF MANPOWER, SINGAPORE, 2003 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanized, photocopying, recording or otherwise, without the prior permission of the copyright holder.
Occupational Safety and Health Division Ministry Of Manpower 18 Havelock Road #03-02 Singapore 059764
Contents
Page
Preface
1
Fundamentals of Sound and Terminology
2
Legal Requirements on Noise Control
13
Cost Benefit Analysis of Noise Control
15
Noise Exposure Limits and Criteria
17
Priority and Methods of Control
22
Plant Planning
27
Engineering Noise Control Materials
34
Noise Barriers
42
Partition Walls
48
Machine Enclosures
54
Personnel Enclosures
64
Room Absorption
66
Damping
70
Noise Control from Material Handling and Vibrating Surfaces
74
Vibration Control
77
Silencers or Mufflers
91
Active Noise Control
102
Preface Noise is one of the prevalent health hazards in industry. Exposure to excessive noise can cause noise-induced deafness or hearing loss - a disease that may take several years to develop and cannot be cured. Fortunately, noise hazard can be controlled. No matter what the noise problems may be in a particular workplace, methods and measures exist to reduce or control the hazard. Noise-induced deafness can therefore be prevented and should be prevented. The main purpose of the guidelines is to provide technical information on how industrial noise can be controlled by engineering means such as the use of barriers, enclosures, partition walls, sound absorbers, damping materials, silencers and isolators. Modification or substitution of noisy processes or equipment and application of innovative technology such as active noise control may also be the solutions to noise control. The first edition of the Guidelines was published in 1985. The second edition was produced in 1999. It was used as one of the main sources of reference in the preparation of the Singapore Standards Code of Practice for Industrial Noise Control. This latest edition updates and refines the guidelines. New sections are added, these include legal requirements on noise control, noise sources identification, cost-benefit of noise control, and specific machinery noise and vibration control. In addition, many diagrams and photos on noise and vibration control are incorporated to showcase engineering controls. The guidelines should help plant engineers, acoustics specialists or service providers, safety and health professionals, technical personnel and people working in the industry who have little knowledge of acoustics but who want to develop a practical approach to controlling noise and vibration problems occurring in the workplaces.
1
1
FUNDAMENTALS OF SOUND AND TERMINOLOGY Sound is generated by vibration of surface or by turbulent fluid flow, which sets the air molecules into motion. It is a wave motion due to air pressure variations. Sound can propagate in gases, liquids and solids, but it cannot propagate in a vacuum. Noise carries the meaning of unwanted sound but the two terms are often used interchangeably. Propagation of Noise When a noise source is placed in an outdoor environment, the sound waves will propagate from the source and there are no boundaries present to reflect the sound waves. However, when it is located within a room or building, the sound waves will be reflected from the boundaries of the room or building. The noise levels which a worker can be subjected to, is influenced by three factors: (1)
The direct field noise from his machinery, or one very near him.
(2)
The reflected or reverberant field noise from one or more machines further away from him.
(3)
The combination of the direct field noise of the nearest machine and reverberant field noise of other machines.
Reflected sound Noise source Direct sound
Fig 1 Propagation of noise in a room
2
Sound Frequency The frequency of sound wave is the rate at which the air pressure variations occur. Frequency is perceived as the pitch of a sound and is expressed in cycles per second (c/s) or Hertz (Hz). Even though sound may consists of a single pure tone, in most cases, it consists of many tones of different frequencies and intensities. Frequency Band (Octave Band and 1/3 – Octave Band) In noise and vibration control, the spectrum of the noise and the vibrations are normally divided into some frequency bands, and each frequency band has an upper frequency limit, a lower frequency limit and a centre frequency. An octave band is a frequency bandwidth that has an upper band-edge frequency equal to twice its lower band-edge frequency. The octave band is the most common frequency bandwidth used for industrial noise control measurements. The standard range of octave bands has the following centre frequencies: 31.5, 63, 125, 250, 500, 1,000, 2,000, 4,000, 8,000 and 16,000 Hz. The standard range of 1/3 – octave bands has the following centre frequencies: 31.5, 40, 50, 63, 80, 100, 125, 160, 200, 250, 315, 400, 500, 630, 800, 1,000, 1,250, 1,600, 2,000, 2,500, 3,150, 4,000, 5,000, 6,300, 8,000, 10,000, 12,500 and 16,000 Hz. Wavelength The wavelength of a sound wave is the distance the wave travels during one cycle. Wavelength is related to frequency by:
λ=
c f
(1)
where λ is the wavelength, m c is the speed of sound, m/s f is the frequency, Hz Low frequency sound has a long wavelength whereas high frequency sound has a short wavelength. Speed of Sound in Air The speed of sound in air is the speed at which the sound waves propagate. It is dependent on temperature and can be calculated by:
3
c = 20 × 273 + T
(2)
where c is the sound speed, m/s T is the temperature, oC The speed of sound in air at room temperature (25 oC) is approximately 345 m/s. Free Field A free field is a region of space where sound waves can propagate without any obstruction. In a free field, sound pressure levels attenuate in accordance with the inverse square law, or with 6 dB attenuation for each doubling of the distance from a point source. Near Field Near field is defined as a region very near a noise source. The near field usually occurs at a distance less than one wavelength from the vibrating surface of the source. In this region, the sound pressure levels do not decrease by 6 dB each time the distance from the source is doubled. Far Field Further away from the source, there is a far field in which the source can be treated as a point source at which the sound pressure levels fall off at a rate of approximately 6 dB per doubling of distance. Direct Field The direct field of a sound source is defined as that part of the sound field, which has not suffered any reflection from any room surfaces or obstacles. In the direct field, the sound level is dominated by the sound directly radiated from the source, and is independent of the room acoustics. Any control of the sound level must be by the direct reduction of the energy or power of the source. Diffused Field Diffused field is a sound field where the sound energy density is nearly uniform throughout the sound field.
Reverberant Field 4
The reverberant field is defined as the area where the reflected sound has a dominant effect on the sound levels. The far field can lead, but not always, into the reverberant field, which fills the rest of the room space. The reverberant field is usually uniform within the room except in the region of the source or near highly absorbing areas. The sound level in the reverberant field is controlled by the power of the source, the size of the room, and the amount of sound absorbing material within the room. Sound Power Level The sound power of a source is the amount of acoustic energy being generated per unit time by the source. The sound power level is defined as: LW = 10 log
W WO
(3)
where LW is the sound power level, dB W is the sound power, watts (W) -12 Wo is the reference sound power of 10 W It should be noted that LW is a constant for a particular source, and is independent of the distance or acoustic environment. Sound Intensity Level Sound intensity is the amount of sound power passing through a unit surface area. The sound intensity level is defined as: LI = 10 log
I IO
(4)
where LI is the sound intensity level, dB I is the sound intensity, W/m2 Io is the reference sound intensity of 10-12 W/m2 Sound Pressure Level Sound pressure refers to the root mean square value of the pressure changes over and below the atmospheric pressure. The sound pressure level is defined as:
5
2
P = 20 log P L P = 10 log P P ref ref where LP is the sound pressure level, dB. P is the sound pressure, pascals (Pa) Pref is the reference pressure, 2 x 10-5 Pa
(5)
The reference pressure is the pressure of the threshold of hearing. LP is dependent on the distance from the source, and the absorption characteristics of the environment “A” Weighting Sound Pressure Level The “A” weighting scale is used to correct the direct noise levels to the levels heard by the ear. This corrected noise level is called dBA and is commonly used in noise measurement. To obtain the dBA levels from the octave band data, the correction factors below must be applied: Table 1 “A” weighting factors Octave Band Centre Frequency (Hz)
31.5
Correction Factor
-39.5 -26.2 -16.2 -8.7
63
125
250
500 -3.3
1K 0
2K
4K
8K
16K
+1.2
+1.0
-1.1
-6.6
Addition of Noise Levels A frequent calculation in noise control engineering involves the addition of noise levels. The formula for calculating the total or combined effect of two or more sound pressure levels is: Li 10
n
LT = 10 log[∑10 ]
(6)
i
where LT is the total sound pressure level, dB or dBA Li is the individual sound pressure level, dB or dBA Example Three machines produce noise levels of 86 dB, 84 dB and 89 dB when operated individually. What is the combined noise level if all the three machines operate simultaneously? The combined noise level is:
6
86
84
89
LT = 10 log[10 10 + 10 10 + 10 10 ] = 10 log[108.6 + 10 8.4 + 10 8.9 ] = 91.6 dB The table below can be used to combine sound levels without using the formula: Table 2 Adding sound pressure levels Difference in noise level
Amount to be added to the higher level
0 1 2 3 4 5 6 7 8 9 10
3.0 2.5 2.1 1.8 1.5 1.2 1.0 0.8 0.6 0.5 0.4
Example If two independent noises with levels of 83 and 87 dB are produced at the same time at a given point, the combined noise level will be 87 + 1.5 = 88.5 dB, since the amount to be added to the higher level, for a difference of 4 dB between the two levels, is 1.5 dB. Subtraction of Noise Levels Sometimes it may be necessary to subtract one noise level from another, for example, when background noise must be subtracted from combined noise to obtain the sound produced by the machine alone. The method used is similar to that described in the addition of noise. Example The noise level measured at a particular location in a factory with a noisy machine operating nearby is 92 dBA. When the machine is turned off, the noise level measured is 88 dBA. What is the level due to the machine alone?
7
Machine noise is: 92 10
88 10
LT = 10 log[10 − 10 ] = 10 log[109.2 − 108.8 ] = 89.8 dB For noise-testing purposes, this procedure should be used only when the total noise exceeds the background noise by 3 dB or more. If the difference is less than 3 dB, a valid sound test probably cannot be made. Combining Octave Band Levels The above method can also be used to combine individual octave band readings to obtain the overall noise level. The appropriate “A” weighting factors (Table 1) are first applied to each octave band sound level and the A-weighted sound level are then combined using the above method. Example If the following octave band readings are predicted in a design calculation, the overall noise level can be estimated as follows: Frequency (Hz)
Sound level (dB)
“A” weighting factor
A-weighted level (dBA)
31.5 63 125 250 500 1K 2K 4K 8K 16K
74 66 71 61 60 75 82 80 87 90
-39.5 -26.2 -16.2 - 8.7 - 3.3 0 + 1.2 + 1.0 - 1.1 - 6.6
34.5 39.8 54.8 52.3 56.7 75.0 83.2 81.0 85.9 83.4
n
Li 10
LT = 10 log[∑10 ] i
= 10 log[10 = 90 dBA
34.5 10
39.8
54.8
52.3
56.7
75
83.2
81
85.9
83.4
+ 10 10 + 10 10 + 10 10 + 10 10 + 10 10 + 10 10 + 10 10 + 10 10 + 10 10 ]
8
Directivity Factor The directivity factor, Q is a measure of the degree to which sound is concentrated in a certain direction rather than radiated evenly in a full spherical pattern. It is defined as: Q=
Iθ Is
(7)
Where Iθ is the sound intensity at some distance from the source and at an angle θ to a specified axis of a directional noise source Is is the sound intensity produced at the same distance from a uniformly radiating sound source of equal sound power For free field radiation, that is, where there are no reflections of sound, Q = 1. For hemispherical radiation of sound, such as in areas where the sound source is on the floor of a room or at ground level in the outdoors, such that ½ spherical radiation exists, Q = 2. If the sound source is near the intersection of the floor and a wall of a room such that ¼ spherical radiation exists, Q would be 4. If the sound source is near the intersection of the floor and two walls such that 1/8 spherical radiation exists, Q would equal 8.
Q=1
Q=8
Q=4 Q=2
Fig 2 Directivity factor of noise source at different locations in a room Sometimes the sound source itself might have a directional radiation pattern. If so, this would have to be taken into account in addition to the environmental radiation pattern discussed above. Room Constant The room constant is a measure of the ability of a room to absorb sound. It can be calculated by the following equation:
9
_
R=
αS
(8)
_
1−α 2 where R is the room constant, m sabins S is the total surface area of the room, m
2
_
α is the average absorption coefficient of the room surface. _
α can be calculated as follows: _
α=
α 1 S1 + α 2 S 2 + .... + α n S n S1 + S 2 + .... + S n
α i Si i =1 S i n
=∑
(9) 2
where Si is the area of each absorbing surface, m α i is the corresponding absorption coefficient of the surface Example Calculate the average absorption coefficient and the room constant, at 1000 Hz of a room 15 m long, 10 m wide and 4 m high; The floor is painted concrete, the ceiling is smooth finish plaster, and the walls are of wood panelling.
Floor Ceiling Side walls End walls Total:
_
α = =
∑α
i
Surface area 2 Si (m )
Absorption coefficient, αi
α i Si
15x10 15x10 (15x4) x 2 (10x4) x 2 -----------500 =======
0.07 0.03 0.09 0.09
10.5 4.5 10.8 7.2 ------33 ====
Si
S 15 * 10 * 0.07 + 15 * 10 * 0.03 + 15 * 4 * 2 * 0.09 + 10 * 4 * 2 * 0.09 500
= 0.66 _
R =
α S _
1−α
=
0 . 066 × 500 1 − 0 . 066
= 35 m2 sabins
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Reverberation Time and Room Absorption The term “αS” in equation (8) is known as room absorption “A”. Room absorption is related to the decay rate of reflected sound which is commonly measured in terms of reverberation time, T60. T60 = 0.161 V / A
(10) 3
where V is the room volume in m . Reverberation time is defined, as the time required for the average sound pressure level to decay 60 dB, or in terms of sound pressure, to 1/1000th of its original value after the sound source has been shut off. In practice, reverberation time can be measured by noting the time required for an impulsive sound to decay 60 dB from its original or peak value. Example 3 The reverberation time in a 12 m x 10 m x 3 m or 360 m room is 1.7 s, the room absorption is: A = 0.161 x 360/1.7 = 34 metric sabins The total surface area of the room is {(12x10) + (12x3) + (10x3)} x 2 2 = 372 m , its average absorption coefficient is: _
α = 34/372 = 0.09 Relationship between Sound Pressure Level and Sound Power Level Many industrial noise problems are complicated by the fact that the noise is confined in a room. Reflections from the wall, floor, ceiling and equipment in the room change the sound wave characteristics from those for free field radiation. The relationship between the sound pressure level and the sound power level is: 4 Q + ] LP = LW + 10 log[ 2 (11) R 4πr where LP is the sound pressure level, dB LW is the sound power level, dB Q is the directivity factor of the sound source 2 R is the room constant, m sabins r is the distance in m from the source to the point where LP is determined 11
Fig. 3 can be used as a quick guide to determine if sound absorption treatment reduces the noise level at a given location.
Figure 3 Relative sound pressure levels versus distance from the source Example Suppose a new machine is placed on the floor of a room. The room has a 2 total surface area of 200 m and the average absorption coefficient is 0.2. A sound power level of the machine is 94 dB. The directivity factor Q = 2, and 2 the room constant R = (0.2 x 200)/(1-0.2) or 50 m sabins. The sound pressure level is:
Q 4 + ] 2 R 4πr 2 4 94 = Lp − 10 log[ + ] 2 4π 2 50
LW = LP − 10 log[
Lp = 85 dB
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