The distance from observer A of intensity of sound 59 db is 28.64 m and the distance from observer B of intensity of sound 83 db is 11.36m
Explanation:
Let's solve this problem in parts
let's start by finding the intensity of the sound in each observer
observer A β = 59 db
β =
where I₀ = W / m²
=
W / m²
Similarly for Observer b
now we use that the emitted power that is constant is the intensity over the area of the sphere where the sound is distributed
P = I A
therefore for the two observers
the area of a sphere is
we substitute the above formula, we get
Let us call the distance from the observer A be to stereo speaker = x, so the distance from the observer B to the stereo speaker = 40- x; we substitute
after solving the above equation we get x = 28.64 m
This is the distance of observer A
similarly The distance from observer B is 35 - x
= 40 - 28.64
= 11.36m
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