Question

A stereo speaker is placed between two observers who are 40 m apart, along the line connecting them. if one observer records an intensity level of 59 db, and the other records an intensity level of 83 db, how far is the speaker from each observer?

Answer 1

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 = $10 log\frac{I_a}{I_o}$

where I₀ = $1 \times 10^{-12}$  W / m²

             $I_a = I_b \times 10 ^{ \frac{\beta}{10} }$

             $I_a = 1\times 10 ^{-12} \times 10 ^{ \frac{59}{10} }$

             $I_a$ = $2.51 \times 10 ^{-6}$ W / m²

Similarly for Observer b $I_b = 3.16 \times 10 ^ {-4}$

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

$A= 4\pi \times r^2$

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

            $I_a (35 -x) ^2 = I_b x^2$

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

To know more about intensity of sound with the given link

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