HW36 - homework 36 PAPAGEORGE MATT Due 4:00 am The sound...

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homework 36 – PAPAGEORGE, MATT – 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 256 m from the explosion the acoustic pressure reaches a maximum of 9 . 09 N / m 2 . The density of the air is 1 . 51 kg / m 3 and the speed of sound is 343 m / s and sound waves in air are absorbed at a rate of approximately 9 . 98 dB / km. What will be the sound level at a distance 6 . 31 km from the explosion? Consider the atmosphere to be homogeneous over the dis- tances considered. Correct answer: 20 . 7636 dB (tolerance ± 1 %). Explanation: Let : λ β = 9 . 98 dB / km , L 1 = 256 m , P m = 9 . 09 N / m 2 , ρ = 1 . 51 kg / m 3 , v = 343 m / s , and L 2 = 6 . 31 km . The intensity at L 1 is I 1 = P 2 m 2 ρ v = (9 . 09 N / m 2 ) 2 2 (1 . 51 kg / m 3 ) (343 m / s) = 0 . 0797676 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 . 0797676 W / m 2 ) (256 m) 2 (6 . 31 km) 2 = 0 . 000131295 W / m 2 . The sound level at L 2 is β 2 = 10 log parenleftbigg I 2 I 0 parenrightbigg = 10 log parenleftbigg 0 . 000131295 W / m 2 1 × 10 12 W / m 2 parenrightbigg = 81 . 1825 dB , so allowing for absorption of the wave over the distance traveled, β 2 = β 2 - λ β ( L 2 - L 1 ) = 81 . 1825 dB - (9 . 98 dB / km) (6 . 31 km - 0 . 256 km) = 20 . 7636 dB . Question 2, chap 17, sect 2. part 1 of 1 10 points A rock band plays at a 68 dB sound level. How many times greater is the sound pressure from another rock band playing at 102 dB? Correct answer: 50 . 1187 (tolerance ± 1 %). Explanation: Let : β 1 = 68 dB and β 2 = 102 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 (102 dB 68 dB) / (20 dB) = 50 . 1187 . 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

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homework 36 – PAPAGEORGE, MATT – 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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