A jet airplane has an intensity of 109.7 W/ m2 when heard at a distance of 26.8 m. What is the maximum sound intensity heard by a person on the ground when the airplane is 8500 m overhead?
Intensity(1) x Area(1) = Intensity(2) x Area(2)
109.7 x (pi(26.8)^2) = Intesity(2) x (pi(8500)^2)
Intensity(2) = 1.09 x 10^-3
To determine the maximum sound intensity heard by a person on the ground when the airplane is 8500 m overhead, we can use the inverse square law for sound intensity. The inverse square law states that the intensity of sound decreases proportionally to the square of the distance from the source.
First, let's find the ratio of the distances:
Distance ratio = (distance on the ground) / (distance overhead)
= 26.8 m / 8500 m
Next, let's calculate the sound intensity ratio using the distance ratio:
Sound intensity ratio = 1 / (distance ratio)^2
Now, we can find the maximum sound intensity on the ground by multiplying the given intensity of the airplane by the sound intensity ratio:
Maximum sound intensity on the ground = (sound intensity of the airplane) * (sound intensity ratio)
Plugging in the given values:
Maximum sound intensity on the ground = 109.7 W/m^2 * (1 / (26.8 m / 8500 m)^2)
Evaluating the expression inside the parentheses:
Maximum sound intensity on the ground = 109.7 W/m^2 * (1 / (26.8 / 8500)^2)
We can simplify the expression inside the parentheses further by squaring the fraction:
Maximum sound intensity on the ground = 109.7 W/m^2 * (1 / ((26.8 / 8500) * (26.8 / 8500)))
Finally, we can calculate the maximum sound intensity on the ground:
Maximum sound intensity on the ground = 109.7 W/m^2 * (1 / (0.00315294)^2)
Maximum sound intensity on the ground ≈ 11,020,785.20 W/m^2
Therefore, the maximum sound intensity heard by a person on the ground when the airplane is 8500 m overhead is approximately 11,020,785.20 W/m^2.