Noise levels in the workplaces

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Solution.

1. According to GOST 12.1.003-2014 [16] determine permissible levels of noise in the workplace laboratories L₆₃ = 91 dB; L₁₂₅ = 83 dB B; L₂₅₀ = 77 dB; L₅₀₀ = 73 dB; L₁₀₀₀ =70 dB; L₂₀₀₀ =68 dB; L₄₀₀₀ = 66 dB and L₈₀₀₀ = 64 dB. We conclude that at certain frequencies, the sound pressure level is exceeded by 1-4 dB, so it is necessary to use sound-absorbing facings in the room.

2. Find the room volume:

m³.

3. Then we calculate the area of the enclosing surfaces of the room:

 m².

4. We determine the constant of an acoustically untreated room for an octave band with an average geometric frequency of 63 Hz by formula (2.2):

B₆₃ = B₁₀₀₀·μ = 0,65 ·V/10 = 0,65 · 216/10 = 14,04 м².

Similarly, we get for other octave bands:

B ₁₂₅ = 13,39 m²;

B ₂₀₀₀ = 32,4 m²;

B₂₅₀= 13,82 m²;

В₄₀₀₀ = 51,84 m² ;

B ₅₀₀=16,2 m²;

B ₈₀₀₀ = 90,72 m².

B ₁₀₀₀ = 21,6 m²;

5. The equivalent sound absorption area for an octave band with an average 63 Hz frequency geometric formula (4.3):

m²

Similarly, we get for other octave bands:

A₁₂₅= 12,7 m²;

A₂₀₀₀ = 28,7 m²;  

A₂₅₀= 13,1 m²;  

A₄₀₀₀= 43,0 m²;

A₅₀₀= 15,2 m²;  

A₈₀₀₀ = 66,7 m².

A₁₀₀₀=19,9 m²;  

6. The distance from the noise sources at which the sound pressure level of the reflected sound is equal to the sound pressure level of the direct sound emitted by these sources is calculated by the formula (4.4):

m,

where n = 4 is the number of identical noise sources in the room.

7. The average coefficient of sound absorption in the room before its acoustic processing for an octave band with an average geometric frequency of 63 Hz is calculated by the formula (4.8):

α₆₃ = В₆₃/(В₆₃ + S) = 14,04/(14,04 + 252) = 0,053.

Similarly, after performing calculations for the remaining octave bands, we obtain:

α₁₂₅ = 0,05;

α₂₀₀₀ = 0,114;

α₂₅₀ = 0,052;

α₄₀₀₀= 0,171,

α₅₀₀ = 0,06;

α₈₀₀₀= 0,265.

α₁₀₀₀ = 0,079;

8. The equivalent area of sound absorption by surfaces not occupied by sound-absorbing lining for an octave band with an average geometric frequency of 63 Hz is calculated by the formula (4.7):

А₁₆₃ = α₆₃ (S – S_o) = 0,053(252 – 180) = 3,8 m²,

where S₀= 180 m² – area surfaces coated with full lining the walls and ceiling.

For the remaining octave bands the order of calculation is similar:

 А_{1 125}= 3,6 m²;

А_{1 2000} = 8,2 m²;

А_{1 250} = 3,7 m²;

А_{1 4000} = 12,3 m²;

А_{1 500} = 4 3 m²;

А_{1 8000}= 19,1 m².

А_{1 1000}= 5,7 m²;

9. The total additional area of sound absorption from the design of sound-absorbing lining for an octave band with an average geometric frequency of 63 Hz, formula (4.10):

ΔА₆₃= α_{0 63} ·S₀ = 0,21·180 = 37,8 m²,

where α_{0 63} = 0,21 – coefficient of sound absorption of perforated panels  of 3 cm thick with asbestos wool inside of 6 mm thick (the values of α₀ for the remaining octave bands are shown in Table 4.4). Similarly we get for the remaining octave bands:

 ΔА₁₂₅ = 93,6 m²;

ΔА₂₀₀₀= 73,8 m²;

ΔА₂₅₀ =97,2 m²;

ΔА₄₀₀₀= 59,4 m²;

ΔА₅₀₀ = 97,2 m²;

ΔА₈₀₀₀= 57,6 m².

ΔА₁₀₀₀= 90 m²;

10. The average sound absorption coefficient of an acoustically processed room in an octave band with an average geometric frequency of 63 Hz, formula (4.9):

α_{1 63} =(Α_{1 63} +ΔA₆₃)/S= (3,8 + 37,8)/252 = 0,165.

Similarly calculate the α₁ for the remaining octave bands:

α_{1 125} = 0,386;

α_{1 2000}= 0,325;

α₂₅₀= 0,4;

α_{1 4000} = 0,285;

α_{1 500} = 0,403;

α_{1 8000}=0,304.

α_{1 1000}= 0,38;

11. The constant of the premise after its facing with sound-absorbing materials for an octave band with an average geometric frequency of
63 Hz, formula (2.6):

В'₆₃ = (А_{1 63} + ΔА₆₃) / (1 - α_{1 63}) = (3,8 + 37,8) / (1 - 0,165) = 49,8 m².

Similarly we calculate В' for the remaining octave bands:

В'₁₂₅= 158,3 m²;

В'₂₀₀₀= 121,5m²;

В'₂₅₀ = 168,2 m²;

В'₄₀₀₀= 100,3m²;

В'₅₀₀=170m²;

В'₈₀₀₀ = 110,2m².

В'₁₀₀₀= 154,4 m²;

  12. The maximum reduction in the sound pressure level in the octave band with the average geometric frequency of 63 Hz with the use of sound-absorbing coatings at the calculated point located in the zone of reflected sound (at a distance from noise sources exceeding 0.95 m), formula (4.5):

ΔL₆₃ = 10 lg(В'₆₃/ В₆₃) = 10 lg(49,8/14,04) = 5,5 dB.

Similarly we get for the rest remaining octave bands:

ΔL₁₂₅= 10,7 dB;

ΔL₂₀₀₀ = 5,7 dB;

ΔL₂₅₀= 10,9 dB;

ΔL₄₀₀₀= 2,8 dB;

ΔL₅₀₀= 10,2 dB;

ΔL₈₀₀₀ = 0,8 dB.

ΔL₁₀₀₀= 8,5 dB;

13. We shall determine the sound pressure levels for octave bands achieved as a result of using the laboratory cladding with sound-absorbing material, and the results will be listed in table 4.6.

Table 4.6

Noise level

Sound pressure level, dB, at frequencies

Achieved

68,5

67,3

70,1

64,8

63,5

63,3

64,2

62,2

Pemissible

14. Conclusion: from table 4.6 it can be seen that, as a result of using perforated panels 3 cm thick with asbestos wool of 6 mm thick inside as a facing surface, complete reduction of the walls and ceiling at all octave frequencies resulted in a decrease in the noise level, which indicates the effectiveness of the sound-absorbing cladding of this type.

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