# The intensity level of sound B, measured in decibels, is given by the equation `B = 10 log( I/I_o)` , where I is the sound intesntiy and Io is a reference defined as the lowest intensity detected...

The intensity level of sound B, measured in decibels, is given by the equation `B = 10 log( I/I_o)` , where I is the sound intesntiy and Io is a reference defined as the lowest intensity detected by the human ear. If Io is as 10^-12 watts per square meter, what is the decibel intesntiy level of a sound measuring 5 watts per square meter?

lemjay | High School Teacher | (Level 2) Senior Educator

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To solve for sound intenity level in decibels (B), plug-in `I_o=10^(-12)` and `I=5` to the given formula.

`B= 10 log(I/I_o)=10log(5/10^(-12))`

To simplify the argument of loagrithm, apply the negative exponent rule which is `a^(-m)=1/a^m` .

`B=10 log (5/(1/10^12)) = 10 log(5*10^12)`

Then, use a calculator to compute for `log (5*10^12)` .

`B=10 xx12.69897=126.9897`

Hence, the intensity level of a sound measuring `5 W/m^2` is 126.9897 dB.