Answer:
a) I = 5,507 10⁻⁴ W / m²
, b) P = 1.65 10⁻⁸ W / m²
, c) R = 4.06 m, I = 1,259 10⁻⁶ W / m²
Explanation:
A) the intensity is defined as the power per unit area
I = P / A
The intensity for the radius of the sphere of 85 m is
A = 4π R²
A = 4π 85²
A = 9,079 10⁴ m²
The intensity at this point is
I = 50.0 / 9.079 10⁴
I = 5,507 10⁻⁴ W / m²
b) The power collected by the microphone
We reduce the area to the SI system
a = 0.30 cm² (1 m / 10² cm)² = 0.3 10⁻⁴ m²
P = I A
P = 5,507 10-4 0.30 10-4
P = 1.65 10⁻⁸ W / m²
c) Let's reduce dβ
β = 10 log (I / I₀)
β = 10 log (5,507 10⁻⁴ / 1 10⁻¹²)
β = 59 dB
d) if the gain is 3 dB, the total intensity is
β = 59 + 3
β = 61 dB
We look for the intensity
I = I₀ 10 β / 10
I = 1 10⁻¹² 10 (61/10)
I = 1,259 10⁻⁶ W / m²
Use
A₁ I₁ = A₂ I₂
A = 4pi R2
We replace
R₁² I₁ = R₂² I₂
R₂ = R₁ √ I₁ / I₂
R = 85 RA (1,259 10⁻⁶ / 5,507 10⁻⁴)
R = 4.06 m
