Question

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?

Answer 1

$\bf \qquad \qquad \textit{inverse proportional variation}\\\\ \textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby \begin{array}{llll} k=constant\ of\\ variation \end{array}\\\\ -------------------------------$

$\bf \begin{array}{llll} \textit{Sound intensity is inversely proportional}\\ \textit{to the square of the distance from the source} \end{array}\implies s=\cfrac{k}{d^2} \\\\\\ \textit{we also know that } \begin{cases} s=30\\ d=8 \end{cases}\implies 30=\cfrac{k}{8^2}\implies 8^2\cdot 30=k \\\\\\ \boxed{1920=k}\qquad thus\qquad s=\cfrac{1920}{d^2} \\\\\\ \textit{what's "s" when d = 4?}\qquad s=\cfrac{1920}{4^2}$