On the decibel scale, the loUdness of a sound, D, in decibels, is given by D=10log I/I_0 where I is the intensity of the sound, in watts per meter^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).

caritatsjq 2022-10-15 Answered
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).
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Answers (1)

indivisast7
Answered 2022-10-16 Author has 13 answers
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)
=120
Therefore, the loudness of a sound with intensity of 10 12 I 0 is 120 decibels
Result:
120 decibels
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