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

2.83m

Step-by-step 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:

`((r_(2))/(r_(1)) )^2=(I_(1))/(I_(2))`

we solve for
`r_(2)`:

`(r_(2))/(r_(1))=\sqrt{(I_(1))/(I_(2)) }\\\\r_(2)=r_(1)\sqrt{(I_(1))/(I_(2)) }`

and we substitute the known values:

`r_(2)=(2m)\sqrt{(80dB)/(40dB) }\\\\r_(2)=(2m)√(2)\\ r_(2)=2.83m`

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