On the decibel scale, the loUdness of a sound, D, in decibels, is given by D = 10 log ⁡ I I 0 where I is the intensity of the sound, in watts per m e t e r 2 , and I 0 is the intensity of a sound barely audible to the human ear. If the intensity of a sound is 10 12 I 0 what is its loudness in decibels? (Such a sound is potentially damaging to the ear).

Question

On the decibel scale, the loUdness of a sound, D, in decibels, is given by   D  =  10  log  ⁡      I          I              0             where I is the intensity of the sound, in watts per   m  e  t  e      r          2      , and       I          0       is the intensity of a sound barely audible to the human ear. If the intensity of a sound is       10          12            I          0       what is its loudness in decibels? (Such a sound is potentially damaging to the ear).

indivisast7 · Accepted Answer

In solving this, sibstitute I by       10          12            I          0        D  =  10  log  ⁡  (                    10                  12                            I                  0                            I              0              )  =  10  log  ⁡      10          12      Apply the property   log  ⁡      10          x        =  x  :D=10(12)=120Therefore, the loudness of a sound with intensity of       10          12            I          0       is 120 decibelsResult:120 decibels

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