Decibels and Distance Loss

The formula depends on the kind of quantity. Power ratios, such as amplifier watts, use ten times the logarithm of the ratio, while voltage and sound-pressure ratios use twenty times the logarithm. It follows that +3 dB doubles the power and +6 dB doubles the voltage or the sound pressure. Perceived loudness grows more slowly: an increase of about +10 dB, which is ten times the power, is commonly perceived as "twice as loud", the relationship described by the sone scale of S. S. Stevens.

A level in decibels needs a stated reference, which the suffix of the unit gives. 0 dBu refers to 0.775 volts, 0 dBV to 1 volt, and 0 dB SPL to 20 micropascals, roughly the quietest sound a healthy ear can detect. dBFS is referenced to the highest level a digital system can represent, so its readings are zero or negative.

Level also changes with distance in a predictable way. In a free field, a point source follows the inverse-square law, and its level falls by about 6 dB each time the distance doubles. A loudspeaker rated at 100 dB at 1 m, the usual reference distance on specification sheets, produces about 94 dB at 2 m, 88 dB at 4 m and 80 dB at 10 m. The front rows of an audience therefore receive much more level than the back rows. Raising the system level does not reduce that gap and only increases the level at the front, so coverage is extended with additional sources such as delay towers and fill loudspeakers. A line array behaves differently in its near field, where the wavefront is close to cylindrical and the level falls by about 3 dB per doubling of distance. The extent of that near field grows with the length of the array and with frequency, and beyond it the loss returns to about 6 dB per doubling.