(Extra Credit) ( Tentatively 10 points) A firework shell explodes a distance h =

Question

(Extra Credit) ( Tentatively 10 points) A firework shell explodes a distance h = 111 m above the ground, creating a colorful display of sparks and a loud sound. Person A standing at point A directly below the explosion detects a sound level of 110 db. Person B stands a distance D to the right of person A and detects a sound level of 102 dB. (a) (6 points) What is the distance D? (b) (4 points) How much sooner does person A hear the sound before person B? Could the two people, using only their ears, distinguish the two arrival times? Explain. Assume the speed of sound is 331 m/s.

Please show steps and show the formula that is used to solve.

Explanation / Answer

a)intensity at A be x.so,

110 = 10*log(x/10^-12)

or x = 10^-1

let the intensity at B be y.so,

102 = 10 log(y/10^-12)

or 1.58*10^-2 = y

and intensity is inversely proportional to the square distance.so,

10/1.58 = D^2/111^2

or D = 279.251 m

b)Time difference = (distance)/speed

=(279.251 - 111)/331

=0.508 seconds

c)No, since the speed of sound is constant.

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