Question

The intensity level of a power mower at a distance of 1.0 m is 100 dB. You wake up one morning to find that four of your neighbors are mowing their lawn 20 m from your open bedroom window. What is the intensity level in your bedroom? The intensity level of a power mower at a distance of 1.0 m is 100 dB. You wake up one morning to find that four of your neighbors are mowing their lawn 20 m from your open bedroom window. What is the intensity level in your bedroom?

A. 50 dB

B. 400 dB

C. 104 dB

D. 80 dB

E. 40 dB

Answer 1

Answer:

β₂ = 74 dB,    The answer is D which is the closest

Explanation:

The definition and intensity is the power per unit area

        I = P / A

        P = I A

The emitted power is constant whereby the energy is distributed over the surface of a sphere

       A = 4π R²

We can also write it in two points

      P = I₁ A₁ = I₂ A₂

      I₁ / I₂ = A₂ / A₁

      I₁ / I₂ = 4π R₂² / 4π R₁²

      I₁ / I₂ = R₂² / R₁²

The definition of decibels is

     β = 10 log (I / I₀)

Let's write this equation for the two given points

m = 1m

     β₁ = 10 log (I₁ / I₀)

m = 20m

     β₂ = 10 log (I₂ / I₀)

Let's eliminate  I₀

     β₁ - β₂ = 10 log (I₁ / I₀) - 10 log (I₂ / I₀) = 10 (log (I₁ / I₀) –log (I₂ / I₀))

     β₁ - β₂ = 10 log (I₁ / I₂)

     β₁ - β₂ = 10 log (R₂² / R₁²)

Let's calculate

     100 –β₂ = 10 log (20²/1²)

     β₂ = 100 - 10 log 400

     β₂  = 100 - 26.0

     β₂ = 74 dB

The answer is D which is the closest