CH 26 soln - INTERFERENCE AND DIFFRACTION 26 8 A 9 C 10 B...

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26-1 I NTERFERENCE AND D IFFRACTION 26 Answers to Multiple-Choice Problems 1. C 2. A, C, D 3. B 4. C 5. A 6. A 7. B 8. A 9. C 10. B 11. A 12. B 13. D 14. C 15. C Solutions to Problems 26.1. Set Up: Constructive interference occurs for Destructive interference occurs for For this problem, and The path taken by the person ensures that x is in the range Solve: (a) For 1, 2, 3, 4 the values of x are 150 cm, 116 cm, 82 cm, 48 cm, 14 cm. (b) For 1, 2, 3 the values of x are 133 cm, 99 cm, 65 cm, 31 cm. Reflect: When the path difference is which is one wavelength. When the path difference is 17 cm, which is one-half wavelength. 26.2. Set Up: For radio waves, Constructive interference occurs for Destructive interference occurs for For this problem, and The path taken by the person ensures that x is greater than 50.0 m. Solve: (a) For 1, 2, 3, 4, 53.3 m, 56.5 m, 59.8 m, 63.0 cm. (b) For 1, 2, 3, 4, 54.9 m, 58.2 m, 61.4 m, 64.7 m. 26.3. Set Up: The nature of the interference depends on the path difference. Solve: (a) The person is a distance from A and a distance from B . The path difference is The interference is determined by D and is independent of d . (b) No, the loudness won’t change. As he walks, the path difference remains constant. 26.4. Set Up: When she is at the midpoint between the two speakers the path difference is zero. When she walks a distance d toward one speaker, increases by d and decreases by d , so the path difference changes by 2 d . gives constructive interference and gives destructive interference. 6 2, c . 6 1, m 5 0, path difference 5 A m 1 1 2 B l , 6 2, c . 6 1, m 5 0, path difference 5 m l , r 1 r 2 r 2 2 r 1 r A 2 r B 5 D 1 d 2 d 5 D . r B 5 d r A 5 D 1 d x 5 51.6 m, m 5 0, x 5 50.0 m 1 A m 1 1 2 B 1 3.26 m 2 . x 2 50.0 m 5 A m 1 1 2 B 1 3.26 m 2 . x 5 50.0 m, m 5 0, x 5 50.0 m 1 m 1 3.26 m 2 . x 2 50.0 m 5 m 1 3.26 m 2 . r 1 5 50.0 m. r 2 5 x 6 2, c . 6 1, m 5 0, r 2 2 r 1 5 A m 1 1 2 B l , 6 2, c . 6 1, m 5 0, r 2 2 r 1 5 m l , l 5 v f 5 3.00 3 10 8 m / s 92.0 3 10 6 Hz 5 3.26 m. v 5 3.00 3 10 8 m / s. x 5 133 cm 150 cm 2 116 cm 5 34 cm, x 5 116 cm m 5 0, x 5 150 cm 2 A m 1 1 2 B 1 34 cm 2 . 150 cm 2 x 5 A m 1 1 2 B 1 34 cm 2 . m 5 0, x 5 150 cm 2 m 1 34 cm 2 . 150 cm 2 x 5 m 1 34 cm 2 . 0 # x # 150 cm. r 1 5 x . r 2 5 150 cm 6 2, c . 6 1, m 5 0, r 2 2 r 1 5 A m 1 1 2 B l , 6 2, c . 6 1, m 5 0, r 2 2 r 1 5 m l ,
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Solve: (a) Path difference is zero, so the interference is constructive. (b) Destructive interference, so the path difference equals and (c) Constructive interference, so path difference equals and 26.5. Set Up: When she is at the midpoint between the two speakers the path difference is zero. When she walks a distance d toward one speaker, increases by d and decreases by d , so the path difference changes by 2 d . Since the speakers are out of phase, gives destructive interference and gives constructive interference. Solve: (a) Path difference is zero, so the interference is destructive. (b) Destructive interference, so the path difference equals and (c) Constructive interference, so the path difference equals and Reflect: When she moves from a point of destructive interference to a point of constructive interference the path dif- ference changes by 26.6.
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