To find out how many miles away the intensity of the sound from the jet aircraft drops to 90 dB, we can use the inverse square law for sound propagation. According to this law, the sound intensity (I) decreases with the square of the distance (r) from the source.
The formula for the inverse square law is as follows:
I1 / I2 = (r2 / r1)^2
where: I1 = Initial sound intensity (in dB) I2 = Final sound intensity (in dB) r1 = Initial distance from the source (in feet) r2 = Final distance from the source (in feet)
Given that the initial sound intensity (I1) is 140 dB and the initial distance (r1) is 100 feet, and we want to find the final distance (r2) where the sound intensity drops to 90 dB (I2 = 90 dB), we can set up the equation as follows:
140 / 90 = (r2 / 100)^2
Now, let's solve for r2:
(140 / 90) = (r2 / 100)^2
(140 / 90) * 100^2 = r2^2
(1.55556) * 10000 = r2^2
15555.6 = r2^2
Now, take the square root of both sides to find r2:
r2 = √15555.6
r2 ≈ 124.75 feet
So, when the intensity of the sound from the jet aircraft drops to 90 dB, it is approximately 124.75 feet away from the source.
To convert this distance to miles, we need to divide by the number of feet in a mile:
1 mile = 5280 feet
r2 (in miles) ≈ 124.75 feet / 5280 feet per mile ≈ 0.0236 miles
Therefore, when the intensity is 90 dB, the distance from the jet aircraft is approximately 0.0236 miles.