Noise Equations

 

Decibels are in Log Scale

 

The best way to understand noise levels is to think of decibels as the log of the noise energy. In other words, a 63 decibel noise is twice as powerful as a 60 decibel noise.

 

When adding decibels: convert to logs first, then back to decibels

 

In this way if you add two noise sources together, you first need to convert their decibels to “energy” levels. For example, a 60 decibel noise has an “energy” of one million and 63 decibel noise has an “energy” of two million.

The calculations below show that adding two noise sources; one with a noise level of 60 decibels and the other with a noise level of 63 decibels; gives a noise level of 64.8 decibels (dB).

 

10(60/10) + 10(63/10) = 106.0 + 106.3 = 1,000,000 + 2,000,000 = 3,000,000

 

10 x log (3,000,000) = 10 x 6.48 = 64.8 dB

 

The Log scale also means that when adding two noise sources that are much different from each other, the louder noise will dominate. For example, when adding 70.0 dB to 57.0 dB the result is 70.2 dB.

 

10(70/10) + 10(57/10) = 107.0 + 105.7 = 10,000,000 + 500,000 = 10,500,000

 

10 x log (10,500,000) = 10 x 7.02 = 70.2 dB

 

The noise level drops 6 decibels when the distance doubles

 

The second most important thing to understand is that the noise energy dissipates in the air by 6 decibels as the distance doubles. The table below gives an illustration.

 

Distance from

noise source (metres)

Noise level at

that distance dB(A)

10

96

20

90

40

84

80

78

160

72

320

66

640

60

 

This relationship can be summarised with the equation below.

 

Drop in dB from Near to Far = 20 x log (Far / Near)

 

For example if the noise from a lawnmower is 75 dB at 10 metres it will be about 61 dB at 50 metres.

 

Drop = 20 x log (50/10) = 20 x log 5 = 20 x 0.7 = 14 dB

 

Noise at 50metres = 75 – Drop = 75 – 14 = 61 dB

 

Other factors influence noise attenuation

 

The 6 dB drop with doubling of distance is the drop in noise due to the energy being dissipated in the air. Noise will also be dissipated by objects, walls, hills, buildings, etc. There is also an impact from temperature and wind but the attenuation due to distance is the primary estimator of the drop in noise level in an outdoor setting.