Question

Architects have to consider how sound travels when designing large buildings such as theaters, auditoriums, or museums. Sound intensity I is inversely proportional to the square of the distance from the sound source d. When the distance is 2, the sound intensity is 4. What is the intensity when the distance is 20

Answer 1

I₂ = 0.04 W / m²

Step-by-step explanation:

Sound intensity is the power emitted between the unit area

I = W / A

W = I A

sound is a wave that travels in space whereby its energy is distributed on the surface of a sphere

A = 4π r²

we substitute

W = I (4π r²)

the emission power is constant, so the intensity at two different points is

W = I₁ 4π r₁² = I₂ 4π r₂²

so the equation is

I₁ r₁² = I₂ r₂²

In this case the units are not shown in the exercise, suppose that all units are in the SI system

I₂ =
`I_1 \ (r_1^2)/(r_2^2)`

let's calculate

I₂ = 4
`4 \ (2^2)/(20^2)`

I₂ = 0.04 W / m²