Measuring/Calculating sound

The dB(A) scale
Public authorities around the world use the so-called dB(A) or decibel (A) , scale to quantify sound measurement. Some examples are given in the table below.
 Sound level dB(A) Threshold of hearing Whisper Talking City traffic Rock concert Jet engine (10m away) 0 30 60 90 120 150

The dB(A) scale measures the sound intensity over the whole range of different audible frequencies (different pitches) and then it uses a weighing scheme which accounts for the fact that the human ear has a different sensitivity to each different sound frequency. Generally, humans hear better at medium, speech range, frequencies than at low or high frequencies. The dB(A) system says, that the sound pressure at the most audible frequencies are to be multiplied by high numbers while the less audible frequencies are multiplied by low numbers and everything is then added up to get an index number. It should be also noted that the (A) weighing scheme is used for weak sounds, such as wind turbines. There exist other weighing schemes for loud sounds called (B) and (C), although they are rarely used.
The dB-scale is a logarithmic, or relative scale. This means, that if the sound pressure, or the energy in the sound, is doubled then the index increases by approximately 3. A sound level of 100 dB(A) thus contains twice the energy of a sound level of 97 dB(A). The reason for measuring sound this way is that our human ears perceive sound in terms of the logarithm of the sound pressure, rather than the sound pressure itself. Most people will say, that if you increase the dB(A) by 10, you double the subjective loudness of the sound.

Sound propagation and distance: Inverse square law
The energy in sound waves, and thus the sound intensity, will drop with the square of the distance to the sound source. In other words, if you move 200 m away from a wind turbine, the sound level will generally be one quarter of what it is 100 m away. A doubling of your distance will thus make the dB(A) level drop by 6.
At one rotor diameter distance (43 m) from the base of a wind turbine emitting 100 dB(A) you will generally have a sound level of 55-60 dB(A) corresponding to a clothes dryer. 4 rotor diameters (170 m) away you will have 44 dB(A), corresponding to a quiet living room in a house. 6 rotor diameters (260 m) away you will have some 40 dB(A).
The precise relationship between sound level and distance from the sound source is given in a table on the Reference Manual on Acoustics. In practice, sound absorption and reflection from soft or hard surfaces may play a role on a particular site and may modify the results shown here.

If we have two wind turbines rather than one, located at the same distance from our ears, naturally the sound energy reaching us will double. As already said, this means that two turbines will increase the sound level by 3 dB(A). Four turbines instead of one, at the same distance, will increase the sound level by 6 dB(A). You will actually need ten turbines placed at the same distance from you, in order to perceive that the subjective loudness has doubled (i.e. the dB level has increased by 10).
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The pure tone penalty
The fact that the human ear (and mind) discerns pure tones more easily than (random) white noise, means the authorities may wish to take that into account when doing sound estimates. They consequently often have rules which specify that you add a certain number to the dB(A) figure in case you have pure tones present in a sound.

Wind turbine information in practice
In accordance with international standards manufacturers generally specify a theoretical dB(A) level for sound emissions which assumes that all sound originates from a central point, although in practice, of course, it will originate from the whole surface of the machine and its rotor. Sound pressure thus calculated is typically around 96-101 dB(A) for modern wind turbines. The figure itself is rather uninteresting, since there will not be a single point, where you can experience that sound level! Rather, it is useful for predicting the sound level at different distances from the wind turbine.
Pure tones have generally be eradicated completely for modern wind turbines, at least in the case of the modern turbines listed in the catalogue on the Wind Power Calculator page.

Legal noise limits
At distances above 300 m the maximum theoretical noise level from high quality wind turbines will generally be significantly below 45 dB(A) outdoors, corresponding to the legislation in Denmark (for built-up areas with several houses, a noise limit of 40 dB(A) is the legal limit in Denmark).
Noise regulations vary from country to country. In practice the same machine designs can be used everywhere.

Current practice: Calculations rather than measurement
Calculating potential sound emission from wind turbines is generally important in order to obtain planning permission (from the public authorities) for installing wind turbines in densely populated areas. Generally speaking, it is far easier to calculate the potential sound emissions than to measure them in practice.
The reason why it is difficult to measure the sound is that the sound level has to be some 10 dB(A) above the background noise in order to measure it properly. The background noise from leaves, birds, and traffic will frequently be above 30 dB(A), however. In most places in the world public authorities therefore rely on calculations rather than measurements, when granting planning permission for wind turbines.

Calculators