Question

The sound from a loud speaker has an intensity level of 80 db at a distance of 2.0m. Consider the speaker to be a point source, how far from the speaker will the sound have an intensity level of 40 db.

Answer 1

Answer:

2.83m

Explanation:

The information that we have is

Intensity at 2.0 m: $I=80dB$ and $r_{1}=2m$

we need an intensity level of: $I_{2}=40dB$

thus, we are looking for the distance $r_{2}$.

which we can find with the law for intensity and distance:

$(\frac{r_{2}}{r_{1}} )^2=\frac{I_{1}}{I_{2}}$

we solve for $r_{2}$:

$\frac{r_{2}}{r_{1}}=\sqrt{\frac{I_{1}}{I_{2}} }\\\\r_{2}=r_{1}\sqrt{\frac{I_{1}}{I_{2}} }$

and we substitute the known values:

$r_{2}=(2m)\sqrt{\frac{80dB}{40dB} }\\\\r_{2}=(2m)\sqrt{2}\\ r_{2}=2.83m$

at a distance of 2.83m the intensity level is 40dB