## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

(a) The intensity at a distance of 1000 meters is $2.5\times 10^{-4}~W/m^2$ (b) The maximum distance at which the siren can be heard is 16 km
(a) We can find the intensity $I_2$ at 1000 m. $\frac{I_2}{I_1} = \frac{r_1^2}{r_2^2}$ $I_2 = I_1~\frac{r_1^2}{r_2^2}$ $I_2 = (0.10~W/m^2)\frac{(50~m)^2}{(1000~m)^2}$ $I_2 = 2.5\times 10^{-4}~W/m^2$ The intensity at a distance of 1000 meters is $2.5\times 10^{-4}~W/m^2$ (b) We can find the maximum distance $r_3$ at which the siren can be heard. $\frac{I_3}{I_1} = \frac{r_1^2}{r_3^2}$ $r_3^2 = \frac{I_1~r_1^2}{I_3}$ $r_3 = \sqrt{\frac{I_1}{I_3}}~r_1$ $r_3 = \sqrt{\frac{0.10~W/m^2}{1\times 10^{-6}~W/m^2}}~(50~m)$ $r_3 = 16,000~m = 16~km$ The maximum distance at which the siren can be heard is 16 km.