HWK36 - homework 36 VALENCIA DANIEL Due 4:00 am The sound...

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homework 36 – VALENCIA, DANIEL – 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 609 m from the explosion the acoustic pressure reaches a maximum of 14 . 1 N / m 2 . The density of the air is 1 . 49 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 . 1 dB / km. What will be the sound level at a distance 4 . 08 km from the explosion? Consider the atmosphere to be homogeneous over the dis- tances considered. Correct answer: 82 . 1373 dB (tolerance ± 1 %). Explanation: Let : λ β = 4 . 1 dB / km , L 1 = 609 m , P m = 14 . 1 N / m 2 , ρ = 1 . 49 kg / m 3 , v = 343 m / s , and L 2 = 4 . 08 km . The intensity at L 1 is I 1 = P 2 m 2 ρ v = (14 . 1 N / m 2 ) 2 2 (1 . 49 kg / m 3 ) (343 m / s) = 0 . 194504 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 . 194504 W / m 2 ) (609 m) 2 (4 . 08 km) 2 = 0 . 00433353 W / m 2 . The sound level at L 2 is β 2 = 10 log parenleftbigg I 2 I 0 parenrightbigg = 10 log parenleftbigg 0 . 00433353 W / m 2 1 × 10 12 W / m 2 parenrightbigg = 96 . 3684 dB , so allowing for absorption of the wave over the distance traveled, β 2 = β 2 - λ β ( L 2 - L 1 ) = 96 . 3684 dB - (4 . 1 dB / km) (4 . 08 km - 0 . 609 km) = 82 . 1373 dB . Question 2, chap 17, sect 2. part 1 of 1 0 points A rock band plays at a 74 dB sound level. How many times greater is the sound pressure from another rock band playing at 114 dB? Correct answer: 100 (tolerance ± 1 %). Explanation: Let : β 1 = 74 dB and β 2 = 114 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 (114 dB 74 dB) / (20 dB) = 100 . 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 – VALENCIA, DANIEL – 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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