How far away can you stand from a jet engine, producing 11,500 W of power, before the sound level crosses the threshold of pain (120 dB)?

To determine how far away you can stand from a jet engine producing 11,500 W of power before the sound level reaches 120 dB, we first need to understand the relationship between sound power and sound intensity levels.

The sound intensity level in decibels (dB) is calculated using the formula:

[ L = 10 \log_{10} \left(\frac{I}{I_0}\right) ]

where ( L ) is the sound level in dB, ( I ) is the intensity in watts per square meter (W/m²), and ( I_0 ) is the reference intensity level, typically taken as ( 1 \times 10^{-12} , \text{W/m}^2 ).

The intensity ( I ) at a distance ( r ) from a point source of sound power ( P ) is given by:

[ I = \frac{P}{4 \pi r^2} ]

Substituting this into the dB formula gives:

[ L = 10 \log_{10} \left(\frac{P}{4 \pi r^2 I_0}\right) ]

For our scenario, we set (