College Algebra, Chapter 5, 5.5, Section 5.5, Problem 38

The sound of a subway train has the intensity of 98 dB. Determine the intensity in $W/m^2$.



Recall that the formula for Sound Intensity in dB is represented as

$\displaystyle B = 10 \log \frac{I}{I_0}$

where

$B$ = intensity level in dB

$I$ = Sound intensity

$I_0 = 10^{-12} W/m^2$ reference intensity

So,


$
\begin{equation}
\begin{aligned}

9.8 =& 10 \log \frac{I}{10^{-12}}
&& \text{Divide each side by } 10
\\
\\
9.8 =& \log \frac{I}{10^{-12}}
&& \text{Take anti log of each side}
\\
\\
10^{9.8} =& \frac{I}{10^{-12}}
&& \text{Multiply each side by } 10^{-12}
\\
\\
I =& 10^{-12} (10^{9.8})
&& \text{Evaluate}
\\
\\
I =& 6.31 \times 10^{-3} \frac{W}{m^2}

\end{aligned}
\end{equation}
$