Answer:
2.83m
Explanation:
The information that we have is
Intensity at 2.0 m: [tex]I=80dB[/tex] and [tex]r_{1}=2m[/tex]
we need an intensity level of: [tex]I_{2}=40dB[/tex]
thus, we are looking for the distance [tex]r_{2}[/tex].
which we can find with the law for intensity and distance:
[tex](\frac{r_{2}}{r_{1}} )^2=\frac{I_{1}}{I_{2}}[/tex]
we solve for [tex]r_{2}[/tex]:
[tex]\frac{r_{2}}{r_{1}}=\sqrt{\frac{I_{1}}{I_{2}} }\\\\r_{2}=r_{1}\sqrt{\frac{I_{1}}{I_{2}} }[/tex]
and we substitute the known values:
[tex]r_{2}=(2m)\sqrt{\frac{80dB}{40dB} }\\\\r_{2}=(2m)\sqrt{2}\\ r_{2}=2.83m[/tex]
at a distance of 2.83m the intensity level is 40dB
