## Decibels The sound intensity The logarithm involved is just the power of ten of the sound intensity expressed as a multiple of the threshold of hearing intensity. Example: If I= 10,000 times the threshold, then the ratio of the intensity to the threshold intensity is 10 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. Decibels provide a relative measure of 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. Another 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.
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## Decibels and LogarithmsThe decibel scale is a reflection of the logarithmic response of the human ear to changes in sound intensity: 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:
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## Decibel CalculationThe sound intensity in decibels above the standard threshold of hearing is calculated as a logarithm. If the intensity as a multiple of threshold is | Index Sound level measurement | ||

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## JND in Sound IntensityA useful general reference is that the just noticeable difference in sound intensity for the human ear is about 1 decibel. 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. That having been established, it can be noted that there are some variations. The jnd is about 1 dB for soft sounds around 30-40 dB at low and midrange freqencies. It may drop to 1/3 to 1/2 a decibel for loud sounds. Caution must be used in applying the "one decibel" criterion. It presumes that you are increasing the
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## Variations in Difference Threshold
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