# 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).

On the decibel scale, the loUdness of a sound, D, in decibels, is given by $D=10\mathrm{log}\frac{I}{{I}_{0}}$ where I is the intensity of the sound, in watts per $mete{r}^{2}$, 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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indivisast7
In solving this, sibstitute I by ${10}^{12}{I}_{0}$
$D=10\mathrm{log}\left(\frac{{10}^{12}{I}_{0}}{{I}_{0}}\right)$
$=10\mathrm{log}{10}^{12}$
Apply the property $\mathrm{log}{10}^{x}=x:$
D=10(12)
=120
Therefore, the loudness of a sound with intensity of ${10}^{12}{I}_{0}$ is 120 decibels
Result:
120 decibels