Answer:
30.25129 m
Explanation:
I = Sound intensity
[tex]\beta[/tex] = Intensity level = 120 dB
[tex]I_0[/tex] = Threshold of human hearing = [tex]10^{-12}\ W/m^2[/tex]
r = Distance
P = Power = 11500 W
Intensity of sound is given by
[tex]\beta=10log\dfrac{I}{I_0}\\\Rightarrow 120=10log\dfrac{I}{10^{-12}}\\\Rightarrow \dfrac{120}{10}=log\dfrac{I}{10^{-12}}\\\Rightarrow 10^{\dfrac{120}{10}}=\dfrac{I}{10^{-12}}\\\Rightarrow I=10^{\dfrac{120}{10}}\times 10^{-12}\\\Rightarrow I=10^{0}\\\Rightarrow I=1\ W/m^2[/tex]
Intensity is given by
[tex]I=\dfrac{P}{4\pi r^2}\\\Rightarrow r=\sqrt{\dfrac{P}{4\pi I}}\\\Rightarrow r=\sqrt{\dfrac{11500}{1\times 4\pi}}\\\Rightarrow r=30.25129\ m[/tex]
The distance is 30.25129 m
