In fact, the use of the factor of 10 in the definition of the decibel is to create a unit which is about the least detectable change in sound intensity. If you know the sound level in decibels at one distance in an open area, then you can estimate the dB level at another distance by making use of the inverse square law.Ī useful general reference is that the just noticeable difference in sound intensity for the human ear is about 1 decibel. Then the difference in decibels is given by I A = dB above I B If one is expressed as a multiple of the other: I A = x I B = x 10^ x I B Then the intensity in decibels is given byĭecibels can also be used to express the relative intensity of two sounds.

If the intensity as a multiple of threshold is The sound intensity in decibels above the standard threshold of hearing is calculated as a logarithm. The logarithm to the base 10 used in this expression is just the power of 10 of the quantity in brackets according to the basic definition of the logarithm: The decibel scale is a reflection of the logarithmic response of the human ear to changes in sound intensity: The unit is based on powers of 10 to give a manageable range of numbers to encompass the wide range of the human hearing response, from the standard threshold of hearing at 1000 Hz to the threshold of pain at some ten trillion times that intensity.Īnother consideration which prompts the use of powers of 10 for sound measurement is the rule of thumb for loudness: it takes about 10 times the intensity to sound twice as loud.

The factor of 10 multiplying the logarithm makes it decibels instead of Bels, and is included because about 1 decibel is the just noticeable difference (JND) in sound intensity for the normal human ear.ĭecibels provide a relative measure of sound intensity. Example: If I = 10,000 times the threshold, then the ratio of the intensity to the threshold intensity is 10 4, the power of ten is 4, and the intensity is 40 dB: The logarithm involved is just the power of ten of the sound intensity expressed as a multiple of the threshold of hearing intensity. The sound intensity I may be expressed in decibels above the standard threshold of hearing I 0.

Decibel sound scale