Answer:
Step-by-step explanation:
To answer the questions, we can use the inverse square law for sound propagation, which states that sound intensity decreases as the square of the distance from the source increases.
(a) To determine the closest distance to preserve your peace of mind with a sound intensity of 1.0 mW/m^2, we can set up the following equation:
Intensity at Distance 1 / Intensity at Distance 2 = (Distance 2)^2 / (Distance 1)^2
Given that the intensity at Distance 1 is 10.0 W/m^2 and the intensity at Distance 2 is 1.0 mW/m^2, we have:
10.0 / 1.0 = (Distance 2)^2 / (Distance 1)^2
Simplifying the equation:
Distance 2^2 = (10.0 / 1.0) * Distance 1^2
Distance 2^2 = 10 * Distance 1^2
Distance 2 = sqrt(10) * Distance 1
Therefore, the closest distance you should live from the airport runway to preserve your peace of mind is the square root of 10 times the initial distance.
(b) If your friend lives twice as far from the runway as you do, her distance would be 2 times your distance. Using the inverse square law, we can calculate the new intensity:
Intensity at Distance 2 = Intensity at Distance 1 * (Distance 1 / Distance 2)^2
Plugging in the values:
Intensity at Distance 2 = 10.0 W/m^2 * (1 / 2)^2
Intensity at Distance 2 = 10.0 * (1 / 4)
Intensity at Distance 2 = 2.5 W/m^2
Therefore, your friend would experience an intensity of 2.5 W/m^2 from the jet.
(c) The power of sound is the rate at which energy is transferred by the sound wave. The intensity of sound is defined as the power per unit area. Given that the intensity at 30.0 m away is 10.0 W/m^2, we can use the formula:
Intensity = Power / (4 * pi * Distance^2)
Solving for power:
Power = Intensity * (4 * pi * Distance^2)
Power = 10.0 W/m^2 * (4 * pi * (30.0 m)^2)
Calculating this equation:
Power ≈ 33929 W
Therefore, the jet plane produces a power of approximately 33929 Watts at takeoff.