Chapter 4, Problem 23CT

The decibel level, $D$, of sound is given by the equation

$D=10\log \left(\frac{I}{I_0}\right)$

Where $I$ is the intensity of the sound and $I_0={10}^{-12}$ watt per square meter.

If the shout of a single person measures $80$ decibels, how loud would the sound be if two people shout at the same time? That is, how loud would the sound be if the intensity doubled?

The pain threshold for sound is 125decibels. If the Athens Olympic Stadium $2004$ ( OlympiakoStadioAthinas “Spyros Louis”) can seat $74,400$ people, how many people in the crowd need to shout at the same time for the resulting sound level to meet or exceed the pain threshold ? (Ignore any possible sound dampening.)