Sound level is measured in decibels (dB).
The equation [tex]\beta = 10\log\left(\frac{I}{I_0}\right)[/tex], where [tex]I_0[/tex] is the intensity of the threshold sound a human can hear ([tex]10^{-12}[/tex] [tex]\text{watts}[/tex]/[tex]\text{meter}^2[/tex]) and [tex]I[/tex] is the intensity of the sound being measured, gives the sound level, [tex]\beta[/tex]
Example:
What was the intensity of the launch of NASA's Saturn V rocket, about 200 dB?
[tex]\beta = 10\log\left(\frac{I}{I_0}\right)\\\\\text{Substitute.} \ 200 = 10\log\left(\frac{I}{10^{-12}}\right)\\\\\text{Isolate the log.} \ 20 = \log\left(\frac{I}{10^{-12}}\right)\\\\\text{Rewrite into exponential form.} \ \frac{I}{10^{-12}} = 10^{20}\\\\\text{Solve for the variable}\\ \ I = (10^{20})(10^{-12}) = 10^8 = 100,000,000 = \text{100 million watts/}m^2[/tex]
