sound intensity is inversely proportional to the square of the distance from the source - the farther from the source you are, the less intense the sound. suppose the sound intensity is 30 watts per square meter (W/m^2) at 8 meters. what is the sound intensity at 4 meters?
[tex]\bf \begin{array}{llll}
\textit{Sound intensity is inversely proportional}\\
\textit{to the square of the distance from the source}
\end{array}\implies s=\cfrac{k}{d^2}
\\\\\\
\textit{we also know that }
\begin{cases}
s=30\\
d=8
\end{cases}\implies 30=\cfrac{k}{8^2}\implies 8^2\cdot 30=k
\\\\\\
\boxed{1920=k}\qquad thus\qquad s=\cfrac{1920}{d^2}
\\\\\\
\textit{what's "s" when d = 4?}\qquad s=\cfrac{1920}{4^2}[/tex]
