Answer:
r₂=0.1 m
Explanation:
Given that
r₁= 10 m , β₁ = 20 dB
At r₂ ,β₂= 60 dB
As we know that intensity level of sound given as
[tex]\beta =10\ log\dfrac{I}{10^{-12}}[/tex]
[tex]\beta _1=10\ log\dfrac{I_1}{10^{-12}}[/tex]
[tex]20=10\ log\dfrac{I_1}{10^{-12}}[/tex]
10² x 10⁻¹² = I₁
I₁=10⁻¹⁰ W/m²
[tex]\beta _2=10\ log\dfrac{I_2}{10^{-12}}[/tex]
[tex]60=10\ log\dfrac{I_1}{10^{-12}}[/tex]
10⁶ x 10⁻¹² = I₂
I₂ = 10⁻⁶ W/m²
I₁=10⁻¹⁰ W/m²
P = I A
P=Power ,I =Intensity ,A=Area
[tex]\dfrac{I_1}{I_2}=\dfrac{r^2_2}{r^2_1}[/tex]
[tex]\dfrac{10^{-10}}{10^{-6}}=\dfrac{r^2_2}{10^2}[/tex]
r₂=0.1 m
