Question

When a certain jet engine is running, 11,500 W of power goes into its deafening roar. How far away from this engine can you stand before the sound level you experience crosses the "threshold of pain," 120 dB? Assume that the engine generates sound equally in all directions.

Answer 1

30.25129 m

Step-by-step explanation:

I = Sound intensity

`\beta` = Intensity level = 120 dB

`I_0` = Threshold of human hearing =
`10^(-12)\ W/m^2`

r = Distance

P = Power = 11500 W

Intensity of sound is given by

`\beta=10log(I)/(I_0)\\\Rightarrow 120=10log(I)/(10^(-12))\\\Rightarrow (120)/(10)=log(I)/(10^(-12))\\\Rightarrow 10^{(120)/(10)}=(I)/(10^(-12))\\\Rightarrow I=10^{(120)/(10)}* 10^(-12)\\\Rightarrow I=10^(0)\\\Rightarrow I=1\ W/m^2`

Intensity is given by

`I=(P)/(4\pi r^2)\\\Rightarrow r=\sqrt{(P)/(4\pi I)}\\\Rightarrow r=\sqrt{(11500)/(1* 4\pi)}\\\Rightarrow r=30.25129\ m`

The distance is 30.25129 m