A jet airplane has an intensity of 92.4 W/ m2 when heard at a distance of 21.2 m. What is the maximum sound intensity heard by a person on the ground when the airplane is 10700 m overhead?
To find the maximum sound intensity heard by a person on the ground when the airplane is 10700 m overhead, we can use the inverse square law for sound intensity. According to the inverse square law, the sound intensity decreases as the square of the distance increases.
The formula for the inverse square law is:
I1 / I2 = (r2 / r1)^2
Where:
I1 = Initial sound intensity
I2 = Final sound intensity
r1 = Initial distance
r2 = Final distance
Let's break down the given information:
Initial sound intensity (I1) = 92.4 W/m^2
Initial distance (r1) = 21.2 m
Final distance (r2) = 10700 m
Now we can plug these values into the formula and solve for the final sound intensity (I2):
I1 / I2 = (r2 / r1)^2
92.4 / I2 = (10700 / 21.2)^2
To find I2, we can rearrange the equation:
I2 = 92.4 / [(10700 / 21.2)^2]
I2 = 92.4 / (503.8^2)
Now we can calculate I2:
I2 = 92.4 / 253,888.4
I2 ≈ 0.0003639 W/m^2
Therefore, the maximum sound intensity heard by a person on the ground when the airplane is 10700 m overhead is approximately 0.0003639 W/m^2.