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HW35 - homework 35 – PAPAGEORGE MATT – Due 4:00 am 1...

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Unformatted text preview: homework 35 – PAPAGEORGE, MATT – Due: Apr 24 2008, 4:00 am 1 Question 1, chap 16, sect 2. part 1 of 3 10 points Two waves in one string are described by the relationships y 1 = A 1 cos( k 1 x- ω 1 t ) y 2 = A 2 sin( k 2 x- ω 2 t ) where A 1 = 3 . 4 cm, A 2 = 4 . 9 cm, k 1 = 6 cm − 1 , k 2 = 4 cm − 1 , ω 1 = 5 rad / s, ω 2 = 3 rad / s, y and x are in centimeters, and t is in seconds. Find the superposition of the waves y 1 + y 2 at the position x 1 = 1 cm and time t 1 = 1 s. Correct answer: 5 . 96024 cm (tolerance ± 1 %). Explanation: At this point we have y 1 = (3 . 4 cm) cos bracketleftBig (6 cm − 1 ) (1 cm)- (5 rad / s) (1 s) bracketrightBig = 1 . 83703 cm y 2 = (4 . 9 cm) sin bracketleftBig (4 cm − 1 ) (1 cm)- (3 rad / s) (1 s) bracketrightBig = 4 . 12321 cm , so y 1 + y 2 = 5 . 96024 cm . Question 2, chap 16, sect 2. part 2 of 3 10 points Find the superposition of the waves y 1 + y 2 at the position x 2 = 1 cm and time t 2 = 0 . 4 s. Correct answer:- . 580946 cm (tolerance ± 1 %). Explanation: At this point we have y 1 = (3 . 4 cm) cos bracketleftBig (6 cm − 1 ) (1 cm)- (5 rad / s) (0 . 4 s) bracketrightBig =- 2 . 22239 cm y 2 = (4 . 9 cm) sin bracketleftBig (4 cm − 1 ) (1 cm)- (3 rad / s) (0 . 4 s) bracketrightBig = 1 . 64144 cm , so y 1 + y 2 =- . 580946 cm . Question 3, chap 16, sect 2. part 3 of 3 10 points Find the superposition of the waves y 1 + y 2 at the position x 3 = 0 . 6 cm and time t 3 = 61 s. Correct answer: 8 . 23271 cm (tolerance ± 1 %). Explanation: At this point we have y 1 = (3 . 4 cm) cos bracketleftBig (6 cm − 1 ) (0 . 6 cm)- (5 rad / s) (61 s) bracketrightBig = 3 . 33694 cm y 2 = (4 . 9 cm) sin bracketleftBig (4 cm − 1 ) (0 . 6 cm)- (3 rad / s) (61 s) bracketrightBig = 4 . 89577 cm , so y 1 + y 2 = 8 . 23271 cm . Question 4, chap 16, sect 3. part 1 of 1 10 points Consider two organ pipes. The first pipe is open at both ends and it’s 2 . 026 m long. The second pipe is open at one end and closed at the other end; it’s 3 . 09 m long. When both pipes are played together, the first overtone — the lowest harmonic above the fundamental frequency — of the second pipe produces beats agains the fundamental harmonic of the first pipe. What is the fre- quency of these beats? Take the sound speed in air to be 336 m / s. homework 35 – PAPAGEORGE, MATT – Due: Apr 24 2008, 4:00 am 2 Correct answer: 1 . 36862 Hz (tolerance ± 1 %)....
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HW35 - homework 35 – PAPAGEORGE MATT – Due 4:00 am 1...

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