Answer to Question #315489 in Mechanics | Relativity for Cato

Question

Matt is watching a jet take off when he hears the engine roar with an intensity of 100 W/m^2. At what minimum distance should Matt be, in order for him to not hear the jet?

Answer 1

Explanations & calculations

• At a distance where the intensity is near his threshold hearing intensity (on average $\small 10^{-12}\,Wm^{-2}$ ) he would not hear the roar.

$\qquad\qquad \begin{aligned} \small 100\,Wm^{-2}&=\small \frac{Power}{4\pi r^2}\\ \small power&=\small 100(4\pi r^2)\\ \\ \small 10^{-12}\,Wm^{-2}&=\small \frac{power}{4\pi x^2}\\ \small x^2&=\small \frac{100(4\pi r^2)}{4\pi.10^{-12}} \\ \small x &=\small 10^7r \end{aligned}$

• He should be at a distance far $\small 10^7$ times where he was initially.