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Unformatted text preview: 261INTERFERENCE ANDDIFFRACTION26Answers to MultipleChoice Problems1.C2.A, C, D3.B4.C5.A6.A7.B8.A9.C10.B11.A12.B13.D14.C15.CSolutions to Problems26.1. Set Up:Constructive interference occurs for Destructive interferenceoccurs for For this problem,and The path taken bythe person ensures that xis in the range Solve: (a)For 1, 2, 3, 4 the values of xare 150 cm,116 cm, 82 cm, 48 cm, 14 cm.(b)For 1, 2, 3 the values of xare 133 cm,99 cm, 65 cm, 31 cm.Reflect:When the path difference is which is one wavelength. Whenthe path difference is 17 cm, which is onehalf wavelength.26.2. Set Up:For radio waves,Constructive interference occurs for Destructive interference occurs forFor this problem,and The path taken by the personensures that xis 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 Aand a distance from B. The path difference isThe interference is determined by Dand 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 shewalks a distance dtoward one speaker,increases by dand decreases by d, so the path difference changes by 2d.gives constructive interference and gives destructive interference.62,c.61,m50,path difference5Am112Bl,62,c.61,m50,path difference5ml,r1r2r22r1rA2rB5D1d2d5D.rB5drA5D1dx551.6 m,m50,x550.0 m1Am112B13.26 m2.x250.0 m5Am112B13.26 m2.x550.0 m,m50,x550.0 m1m13.26 m2.x250.0 m5m13.26 m2.r1550.0 m.r25x62,c.61,m50,r22r15Am112Bl,62,c.61,m50,r22r15ml,l 5vf53.003108m/s92.03106Hz53.26 m.v53.003108m/s.x5133 cm150 cm2116 cm534 cm,x5116 cmm50,x5150 cm2Am112B134 cm2.150 cm2x5Am112B134 cm2.m50,x5150 cm2m134 cm2.150 cm2x5m134 cm2.#x#150 cm.r15x.r25150 cm62,c.61,m50,r22r15Am112Bl,62,c.61,m50,r22r15ml,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 shewalks a distance dtoward one speaker,increases by dand decreases by d, so the path difference changes by 2d.Since the speakers are out of phase,gives destructive interferenceand 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 difference changes by 26.6. Set Up:Since the values of mare rather large, don’t use Eq.(26.6). For bright fringes,For dark fringes,For the fifth bright fringe (not counting the central bright spot),and for the eighth dark fringe,...
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This note was uploaded on 03/01/2009 for the course PHYS PHYS 6C taught by Professor Geller during the Fall '09 term at UCSB.
 Fall '09
 Geller
 Diffraction

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