Sound is a complex of vibrations in diverse frequencies. These vibrations are transmitted by means of a medium. When we talk to each other for example, that medium is the surrounding air.
Unit of sound level
Strictly scientifically speaking, sound is expressed in Pascal (Pa), the unit of pressure. As we are dealing with very low pressures, we generally speak of micropascal or millionths of a pascal. The lowest audible sound pressure for the human ear, the hearing threshold level, corresponds to 20 micropascal. When the human ear experiences sound as being painful, the pressure is about 100 million micropascal, some five million times more. This linear form of expression is rarely used as both figures deviate too much from each other. In this case the decibel unit is employed - dB(A), a much more manageable, logarithmic unit of measure.
Sound between audible and painful
Scientists have agreed that the hearing threshold level corresponds with 0 dB(A). Logarithmically calculated, an increase with 3 dB(A) corresponds with a doubling of the sound level intensity. Suppose that a noise meter indicates 70 dB(A) for a certain machine going at full speed. If a second, identical machine is put next to the first one, the meter will not indicate 140 dB(A) but 73 dB(A). Of course, the reverse is also true. If you want to decrease a certain sound level with 3 dB(A), you have to stop half of the sound source. So if a factory emits noise which is 3 dB(A) too high, theoretically you would have to stop half of the factory.
Noise is a personal matter
How sound and noise are perceived is very personal. Noise that is experienced as being intolerable for one person can be pleasant for another - blaring pop music for example.
Also the point in time is a subjective matter: sound that is experienced as being normal during the day, can cause sleeplessness during the night.
Also the location is relevant: a sound level you accept at the workplace can be annoying in your spare time.
In the end legal standards are the only objective base in this case.