Answer
We can move 5.0 meters closer to the source before the sound intensity reaches the threshold of pain.
Work Step by Step
We can find the radius $r_2$ where the intensity $I_2$ is $1.0~W/m^2$.
$\frac{r_2^2}{r_1^2} = \frac{I_1}{I_2}$
$r_2 = \sqrt{\frac{I_1}{I_2}}~r_1$
$r_2 = \sqrt{\frac{0.11~W/m^2}{1.0~W/m^2}}~(7.5~m)$
$r_2 = 2.5~m$
At a distance of 2.5 meters from the source, the sound intensity reaches the threshold of pain. The distance from 7.5 meters away to 2.5 meters away is 5.0 meters. Therefore, we can move 5.0 meters closer to the source before the sound intensity reaches the threshold of pain.
