REFERENCE MANUAL

Acoustics

Sound levels and sound power
To understand the table below, read the pages starting with Sound from Wind Turbines in the Guided Tour. If you wish to know about designing wind turbines for quiet operation, read the pages on turbine design in the Guided Tour.
The subjective sound loudness is perceived to double every time the dB(A) level increases by 10. By definition the sound level in dB = 10 * log10(power in W/m2) + 120, where log10 is the logarithm function with base 10. If you only have access to the the natural log function, ln, then you can always use the relation log10(x) = ln(x) / ln(10).
If you solve the equation for the power, you get:     the sound power in W/m2 = 100.1*(dB-120)

 Sound [dB(A)] Power [W/m2] Sound [dB(A)] Power [W/m2] Sound [dB(A)] Power [W/m2] Sound [dB(A)] Power [W/m2] 0 1.000*10-12 48 6.310*10-8 69 7.943*10-6 90 1.000*10-3 10 1.000*10-11 49 7.943*10-8 70 1.000*10-5 91 1.259*10-3 20 1.000*10-10 50 1.000*10-7 71 1.259*10-5 92 1.585*10-3 30 1.000*10-9 51 1.259*10-7 72 1.585*10-5 93 1.995*10-3 31 1.259*10-9 52 1.585*10-7 73 1.995*10-5 94 2.512*10-3 32 1.585*10-9 53 1.995*10-7 74 2.512*10-5 95 3.162*10-3 33 1.995*10-9 54 2.512*10-7 75 3.162*10-5 96 3.981*10-3 34 2.512*10-9 55 3.162*10-7 76 3.981*10-5 97 5.012*10-3 35 3.162*10-9 56 3.981*10-7 77 5.012*10-5 98 6.310*10-3 36 3.981*10-9 57 5.012*10-7 78 6.310*10-5 99 7.943*10-3 37 5.012*10-9 58 6.310*10-7 79 7.943*10-5 100 1.000*10-2 38 6.310*10-9 59 7.943*10-7 80 1.000*10-4 101 1.259*10-2 39 7.943*10-9 60 1.000*10-6 81 1.259*10-4 102 1.585*10-2 40 1.000*10-8 61 1.259*10-6 82 1.585*10-4 103 1.995*10-2 41 1.259*10-8 62 1.585*10-6 83 1.995*10-4 104 2.512*10-2 42 1.585*10-8 63 1.995*10-6 84 2.512*10-4 105 3.162*10-2 43 1.995*10-8 64 2.512*10-6 85 3.162*10-4 106 3.981*10-2 44 2.512*10-8 65 3.162*10-6 86 3.981*10-4 107 5.012*10-2 45 3.162*10-8 66 3.981*10-6 87 5.012*10-4 108 6.310*10-2 46 3.981*10-8 67 5.012*10-6 88 6.310*10-4 109 7.943*10-2 47 5.012*10-8 68 6.310*10-6 89 7.943*10-4 110 1.000*10-1

Sound levels by distance from source
How to use the table below: If a wind turbine has a source noise level of 100 dB(A), it will have a noise level of 45 dB(A) 141 m away. [100 - 55 dB(A) = 45 dB(A)].
The sound level decreases by approximately 6 dB(A) [ = 10*log10(2) ] every time you double the distance to the source of the sound. The table assumes that sound reflection and absorption (if any) cancel one another out.
How to derive the table above: The surface of a sphere = 4 pi r2, where pi = 3.14159265, and r is the radius of the sphere. If we have a sound emission with a power of x W/m2 hitting a sphere with a certain radius, then we'll have the same power hitting four times as large an area, if we double the radius.

 Distance [m] Sound level change [dB(A)] Distance [m] Sound level change [dB(A)] Distance [m] Sound level change [dB(A)] 9 -30 100 -52 317 -62 16 -35 112 -53 355 -63 28 -40 126 -54 398 -64 40 -43 141 -55 447 -65 50 -45 159 -56 502 -66 56 -46 178 -57 563 -67 63 -47 200 -58 632 -68 71 -49 224 -59 709 -69 80 -50 251 -60 795 -70 89 -51 282 -61 892 -71

Adding sound levels from two sources
Example: A turbine located at 200 m distance with a source level of 100 dB(A) will give a listener a sound level of 42 dB(A), as we learned in the table before this one. Another turbine 160 m away with the same source level will give a sound level of 44 dB(A) on the same spot. The total sound level experienced from the two turbines will be 46.1 dB(A), according to the table above.
Two identical sound levels added up will give a sound level +3 dB(A) higher. Four turbines will give a sound level 6 dB(A) higher. 10 turbines will give a level 10 dB(A) higher.

dB
41
42
43
44
45
46
47
48
49
50
41
44.0
44.5
45.1
45.8
46.5
47.2
48.0
48.8
49.6
50.5
42
44.5
45.0
45.5
46.1
46.8
47.5
48.2
49.0
49.8
50.6
43
45.1
45.5
46.0
46.5
47.1
47.8
48.5
49.2
50.0
50.8
44
45.8
46.1
46.5
47.0
47.5
48.1
48.8
49.5
50.2
51.0
45
46.5
46.8
47.1
47.5
48.0
48.5
49.1
49.8
50.5
51.2
46
47.2
47.5
47.8
48.1
48.5
49.0
49.5
50.1
50.8
51.5
47
48.0
48.2
48.5
48.8
49.1
49.5
50.0
50.5
51.1
51.8
48
48.8
49.0
49.2
49.5
49.8
50.1
50.5
51.0
51.5
52.1
49
49.6
49.8
50.0
50.2
50.5
50.8
51.1
51.5
52.0
52.5
50
50.5
50.6
50.8
51.0
51.2
51.5
51.8
52.1
52.5
53.0

How to add sound levels in general
For each one of the sound levels at the spot where the listener is located, you look up the sound power in W/m2 in the first of the three sound tables. Then you add the power of the sounds, to get the total no. of W/m2. Then use the formula dB = 10 * log10(power in W/m2) + 120, to get the dB(A) sound level.