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Unformatted text preview: Create assignment, 00224, Homework 11, Apr 11 at 8:10 am 1 This printout should have 17 questions, check that it is complete. Multiplechoice questions may continue on the next column or page: find all choices before making your selection. The due time is Central time. AP B 1998 MC 51 37:02, trigonometry, multiple choice, < 1 min. 001 Plane sound waves of wavelength 0 . 12 m are incident on two narrow slits in a box with nonreflecting walls, as shown. At a distance of 5 m from the center of slits, a firstorder maximum occurs at point P , which is 3 m from the central maximum. Sound = 0.12 m 5.0 m 3.0 m The distance d between the slits is most nearly 1. d = 0 . 07 m. 2. d = 0 . 09 m. 3. d = 0 . 16 m. 4. d = 0 . 20 m. correct 5. d = 0 . 24 m. Explanation: The rules for determining interference max imum or minimum are the same for sound waves and light waves. For the first maximum, = . Since sin d y L , therefore d y L = d L y = L y = (0 . 12 m)(5 m) 3 m = 0 . 2 m . Dark Fringe Distance 37:02, trigonometry, numeric, > 1 min. 002 A screen is illuminated by 500 nm light as shown in the figure below. y 7 5 m . 5mm S 1 S 2 viewing screen How far apart y 7 are the central bright region and the seventh dark fringe? Correct answer: 3 . 25007 cm. Explanation: Let : L = 5 m y = 3 . 25007 cm d = 0 . 5 mm r 2 r 1 y L d S 1 S 2 = ta n 1 y L viewing screen d sin r 2 r 1 P O 6 S 2 QS 1 90 Q Basic Concepts: d sin = m, where m + 1 2 = 0 , 1 , 2 , 3 , . y = L tan . Solution: For the third dark fringe, m = 6, so = arcsin m + 1 2 d Create assignment, 00224, Homework 11, Apr 11 at 8:10 am 2 = arcsin 6 + 1 2 (5 10 7 m) (0 . 0005 m) = 0 . 00650005 rad . The distance is y 7 = L tan = (5 m)tan(0 . 00650005 rad) = 0 . 0325007 m = 3 . 25007 cm . Double Slits 13 37:02, trigonometry, numeric, > 1 min. 003 The slits in a Youngs interference apparatus are illuminated with monochromatic light of wavelength . The third dark band is y from the axis. The two slits are d apart and the screen is L away from the slits. We want to calculate the wavelength of the light used. L d y What is y in terms of ,d and L ? 1. = 3 L d 2. = 5 2 L d correct 3. = 7 2 L d 4. = 2 L d 5. = 5 2 d L 6. = 7 2 d L 7. = 3 d L 8. = 2 d L 9. = L d 10. = d L Explanation: Basic Concepts: The condition for dark fringes (destructive interference) is d sin = m + 1 2 , where, m = 0 , 1 , 2 , . Solution: The position of dark bands in the double slits experiments is given by d sin = m + 1 2 , where m = 0 , 1 , 2 , . Since the angle is very small, we can take the following approximation = sin = tan = y dark L ....
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 Spring '10
 Avram
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