hw 35 - homework 35 HETTIGER, CHRISTOF Due: Apr 24 2008,...

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Unformatted text preview: homework 35 HETTIGER, CHRISTOF 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- 1 t ) y 2 = A 2 sin( k 2 x- 2 t ) where A 1 = 4 . 3 cm, A 2 = 1 . 4 cm, k 1 = 7 cm 1 , k 2 = 3 cm 1 , 1 = 3 rad / s, 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:- 2 . 81067 cm (tolerance 1 %). Explanation: At this point we have y 1 = (4 . 3 cm) cos bracketleftBig (7 cm 1 ) (1 cm)- (3 rad / s) (1 s) bracketrightBig =- 2 . 81067 cm y 2 = (1 . 4 cm) sin bracketleftBig (3 cm 1 ) (1 cm)- (3 rad / s) (1 s) bracketrightBig = 0 cm , so y 1 + y 2 =- 2 . 81067 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 = 0 . 6 cm and time t 2 = . 5 s. Correct answer:- 3 . 47378 cm (tolerance 1 %). Explanation: At this point we have y 1 = (4 . 3 cm) cos bracketleftBig (7 cm 1 ) (0 . 6 cm)- (3 rad / s) (0 . 5 s) bracketrightBig =- 3 . 88751 cm y 2 = (1 . 4 cm) sin bracketleftBig (3 cm 1 ) (0 . 6 cm)- (3 rad / s) (0 . 5 s) bracketrightBig = 0 . 413728 cm , so y 1 + y 2 =- 3 . 47378 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 . 7 cm and time t 3 = 77 s. Correct answer: 3 . 68917 cm (tolerance 1 %). Explanation: At this point we have y 1 = (4 . 3 cm) cos bracketleftBig (7 cm 1 ) (0 . 7 cm)- (3 rad / s) (77 s) bracketrightBig = 4 . 28075 cm y 2 = (1 . 4 cm) sin bracketleftBig (3 cm 1 ) (0 . 7 cm)- (3 rad / s) (77 s) bracketrightBig =- . 591578 cm , so y 1 + y 2 = 3 . 68917 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 its 1 . 657 m long. The second pipe is open at one end and closed at the other end; its 2 . 465 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 339 m / s. homework 35 HETTIGER, CHRISTOF Due: Apr 24 2008, 4:00 am 2 Correct answer: 0 . 850715 Hz (tolerance 1 %)....
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This note was uploaded on 05/09/2010 for the course PHYSICS PHY 301k taught by Professor Turner during the Spring '10 term at University of Texas-Tyler.

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hw 35 - homework 35 HETTIGER, CHRISTOF Due: Apr 24 2008,...

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