At a distance of 30 m the noise from the engine of an jet has an intensity level of 130 dB.
At this level, you will be in pain and your ears will hurt. That's why this intensity is know as the "pain threshold".
How far do you have to be from a jet (total distance in meters), in order for the noise to drop down in intensity to 69 dB, a level comparable to that of a spoken conversation?
To find the distance you need to be from the jet for the noise intensity to drop to 69 dB, we can use the inverse square law formula:
I2 = I1 (d1/d2)^2
Where:
I1 is the initial intensity level (130 dB)
I2 is the final intensity level (69 dB)
d1 is the initial distance (30 m)
d2 is the final distance we need to find.
Rearranging the formula to solve for d2:
d2 = d1 * sqrt(I1/I2)
Plugging in the given values:
d2 = 30 * sqrt(130/69)
Calculating this value:
d2 ≈ 30 * 1.361
Therefore, the distance you need to be from the jet for the noise intensity to drop to 69 dB is approximately 40.83 meters.