# hw 36 - homework 36 – HETTIGER CHRISTOF – Due 4:00 am 1...

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Unformatted text preview: homework 36 – HETTIGER, CHRISTOF – Due: Apr 26 2008, 4:00 am 1 Question 1, chap 17, sect 2. part 1 of 1 10 points An explosive charge is detonated at a height of several kilometers in the atmosphere. At a distance of 549 m from the explosion the acoustic pressure reaches a maximum of 15 . 2 N / m 2 . The density of the air is 1 . 46 kg / m 3 and the speed of sound is 343 m / s and sound waves in air are absorbed at a rate of approximately 4 . 24 dB / km. What will be the sound level at a distance 4 . 05 km from the explosion? Consider the atmosphere to be homogeneous over the dis- tances considered. Correct answer: 81 . 4282 dB (tolerance ± 1 %). Explanation: Let : λ β = 4 . 24 dB / km , L 1 = 549 m , P m = 15 . 2 N / m 2 , ρ = 1 . 46 kg / m 3 , v = 343 m / s , and L 2 = 4 . 05 km . The intensity at L 1 is I 1 = P 2 m 2 ρ v = (15 . 2 N / m 2 ) 2 2 (1 . 46 kg / m 3 ) (343 m / s) = 0 . 23068 W / m 2 . Since the intensity is inversely proportional to the distance squared, I 2 I 1 = L 2 1 L 2 2 I 2 = I 1 L 2 1 L 2 2 = (0 . 23068 W / m 2 ) (549 m) 2 (4 . 05 km) 2 = 0 . 00423882 W / m 2 . The sound level at L 2 is β 2 = 10 log parenleftbigg I 2 I parenrightbigg = 10 log parenleftbigg . 00423882 W / m 2 1 × 10 − 12 W / m 2 parenrightbigg = 96 . 2724 dB , so allowing for absorption of the wave over the distance traveled, β ′ 2 = β 2- λ β ( L 2- L 1 ) = 96 . 2724 dB- (4 . 24 dB / km) (4 . 05 km- . 549 km) = 81 . 4282 dB . Question 2, chap 17, sect 2. part 1 of 1 10 points A rock band plays at a 51 dB sound level. How many times greater is the sound pressure from another rock band playing at 111 dB? Correct answer: 1000 (tolerance ± 1 %). Explanation: Let : β 1 = 51 dB and β 2 = 111 dB . For a given sound level, every increase of 20 dB corresponds to a pressure amplitude 10 times larger than the original pressure ampli- tude, so n = 10 ( β 2 − β 1 ) / 20 = 10 (111 dB − 51 dB) / (20 dB) = 1000 . Question 3, chap 17, sect 2. part 1 of 3 10 points A point source emits sound waves uniformly in all directions with a power output P . r rock concert A homework 36 – HETTIGER, CHRISTOF – Due: Apr 26 2008, 4:00 am 2 What is the intensity of the sound waves detected by a receiver a distance r from the source? Assume the receiver has a cross sec- tion A perpendicular to the direction of the incident sound....
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hw 36 - homework 36 – HETTIGER CHRISTOF – Due 4:00 am 1...

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