Question

A speaker creates uniformly spherical sounds w/ 500 watts of power

Answer 1

Answer:

A) I = 0.09947 W , β = 109 db , B) β = 116 db , β = 116 db , c) Δβ = 7 dB,

D)  P = 50.27 W

Explanation:

A) The intensity of a spherical sound wave is

          I = P / A

where A is the area of ​​the sphere where the sound is distributed

          A = 4π R²

       

we substitute

          I = P / 4πR²

let's calculate

          I = 500 / (4π 20²)

          I = 0.09947 W

to express this quantity in decibels we use relate

         β = 10 log (I / I₀)

The detectivity threshold is I₀ = 1 10⁻¹² W / m²

         β = 10 lob (0.09947 / 10⁻¹²)

         β = 10 (10.9976)

         β = 109 db

B) intensity at r = 10m

          I = 500 / (4π 10²)

          I = 0.3979 W / m²

          β = 10 log (0.3979 / 10⁻¹²)

          β = 10 (11.5997)

          β = 116 db

C) the change in intensity in decibles is

          Δβ = β₁ - β₂

          Δβ = 116 - 109

          Δβ = 7 dB

D) let's find the intensity for 100 db

          I = I₀ 10 (β / 10)

          I = 10⁻¹² 10 (100/10)

          I = 10⁻² W / m²

Thus

           P = I A

           P = I 4π R²

           P = 10⁻² 4π 20²

           P = 50.27 W