A jet airplane has an intensity of 97.7W/ m^2 when heard at a distance of 30.0m. What is the maximum sound intensity heard by a person on the ground when the airplane is 10100m overhead?
To find the maximum sound intensity heard by a person on the ground when the airplane is 10100m overhead, we can use the inverse square law for sound.
The inverse square law states that the intensity of sound decreases as the square of the distance from the source increases. Mathematically, it can be expressed as:
I1 / I2 = (D2 / D1)^2
Where:
I1 is the initial intensity of sound
I2 is the final intensity of sound
D1 is the initial distance from the sound source
D2 is the final distance from the sound source
In this case, we are given the initial intensity (97.7W/m^2) and the initial distance (30.0m). We need to find the final intensity when the distance is 10100m.
Let's plug in the values into the equation:
I1 / I2 = (D2 / D1)^2
97.7 / I2 = (10100 / 30.0)^2
Now we can solve for I2:
I2 = 97.7 / (10100 / 30.0)^2
I2 = 97.7 / (336.667)^2
I2 = 97.7 / 113392.78
I2 ≈ 0.000862 W/m^2
Therefore, the maximum sound intensity heard by a person on the ground when the airplane is 10100m overhead is approximately 0.000862 W/m^2.