To calculate decibels, use the following formula:, where L is loudness and is 10 -12 which is barely audible. We use the standard notation for the solution to ax b.

If you were standing one foot away from a loud machine, for instance, you would experience higher decibel levels than if you were ten feet away, even though the intensity of the sound produced remains unchanged. The intensity of a sound reaching a person's ear depends not only on the intensity of the sound produced, but also on the persons distance from the source of the sound. Though reducing the decibel level produced by a sound source from 80 to 77 may not seem like a major change, it would actually represent a 50% reduction in audible sound. Rather, each three decibel increment affects a 50% change in sound pressure levels.

The logarithm is the inverse function of the exponential function: if x. The intensity is then described as being decibels, abbreviated dB. A sound with a 50 dB level is not twice as intense as a sound with a 25 dB level. The logarithmic expression The most common bases for logarithms are 10, Logarithms have the following properties and identities: A decibel (dB) is defined as. It is very important to note that the unit is logarithmic. where is the base-10 logarithm and is the threshold of hearing. However, the relationship among the values on the decibel scale is not linear but logarithmic. The intensity of sound is measured in a unit called the decibel (dB), which describes the relative intensity of a sound based on a logarithmic scale containing values ranging from 0 to 194.Ī zero value on the decibel scale represents the weakest sound audible to humans and sound intensity increases in correspondence with numeric values.

Decibel logarithmic scale