**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)} = 10^{6.0} + 10^{6.3} = 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)} = 10^{7.0} + 10^{5.7} = 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.