The intensity of the sound wave from an airplane is 1.0 × 102 W/m2 at 5.0 m. What is the intensity at 100 m?
Question
The intensity of the sound wave from an airplane is 1.0 × 10² W/m² at 5.0 m. What is the intensity at 100 m?
Solution
The intensity of a sound wave decreases with the square of the distance from the source. This is known as the inverse square law.
The formula for the inverse square law is:
I2 = I1 * (d1/d2)^2
where: I1 is the initial intensity, I2 is the final intensity, d1 is the initial distance, and d2 is the final distance.
Given in the problem: I1 = 1.0 × 10^2 W/m^2, d1 = 5.0 m, and d2 = 100 m.
Substitute these values into the formula:
I2 = 1.0 × 10^2 W/m^2 * (5.0 m / 100 m)^2 = 1.0 × 10^2 W/m^2 * (0.05)^2 = 1.0 × 10^2 W/m^2 * 0.0025 = 0.25 W/m^2
So, the intensity of the sound wave from the airplane at 100 m is 0.25 W/m^2.
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