A fireworks shell explodes H=110 m above the ground, creating colorful sparks. How much greater is the sound level of the explosion for a person at a point directly below the explosion than for a person a horizontal distance of L=190 m away?
The intensity of the sound waves drops off as 1/r2 where r is the distance from the point where the sound is made. One observer is at a distance r1=110 m; the other is at a distance of r22 = 1102 + 1902 from the explosion.
Take the ratio of observer 1's sound level to observer 2's:
(1/r12) / (1/r22) = r22/r12
Plug in the values of r1 and r2 to solve.
Leigh A.
04/15/14