The intensity of a certain spherical wave is 8.0 W/m² at a distance of 1.0 m from the source. If the medium is isotropic and nonabsorbing, the intensity 100 m from the source is A) 8.0 W/m². B) 6.4  10^-⁴ W/m². C) 1.9  10^-⁴ W/m². D) 8.0  10^-⁴ W/m². E) 1.9  10^-⁶ W/m².

Question

Quizplus · Accepted Answer

According to the inverse square law, the intensity of the wave decreases with the square of the distance from the source. So, the intensity at 100 m is: $$I_{100m}=\frac{8.0W/m^2}{(100m/1m)^2}=8.0\cdot 10^{-4}W/m^2$$ Using the conversion factor of $10^4$ from $m^2$ to $cm^2$ gives: $$I_{100m}=8.0\cdot 10^{-4}\cdot 10^4=8.0\cdot 10^0 W/cm^2$$ which is the same as 8.0 W/m² as given in choice D.

The Intensity of a Certain Spherical Wave Is 8