Interference_worksheet_key

# Interference_worksheet_key - _a‘_ Superposition - CHAPTER...

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Unformatted text preview: _a‘_ Superposition - CHAPTER 21 21-7 KEV 9. The ﬁgure shows a snapshot graph at t = 0 s of loudspeakers emitting triangular—shaped sound waves. Speaker 2 can be moved forward or backward along the axis. Both speakers vibrate in phase at the same frequency. The second speaker is drawn below the ﬁrst, so that the ﬁgure is clear, but you want to think of the two waves as overlapped as they travel along the x-axis. 21.5 Interference in One Dimension 21.6 The Mathematics of Interference a. On the left set of axes, draw the t: 0 s snapshot graph of the second wave if speaker 2 is placed at each of the positions shown. The ﬁrst graph, with xspeaker = 2 m, is already drawn. 4 m #1 “ —> I I I I I I I I x (m) —4 4 8 I: 0 Net wave to the right of bark speakers l 51 It #2 p I I I I I I I r I X l I —4 0 4 —4 O 4 8 —> #2 #1 I I I | I I I I I I I I' I I )5 I I I T I I -4 4 8 / 4/1 I’ng U #2 i #1 w KW ’ E W I I I i I I T . I I I I I I X h x (m) ~4 0 4 8 —4 4 #2 I i‘x(m) 8 ‘ #1 \\ I l I I I I l I I I I I l I I I I I 'I X0“) 0 4 8 —4 4 b. On the right set of axes, draw the superposition Dnet = D] + D2 of the waves from the two speakers. Dnet exists only to the right of both speakers. It is the net wave traveling to the right. , , C. What separauons between the speakers glve constructive interference? :9 r7 f d. What are the Ax/A ratios at the points of constructive interference? _~_.J___ e. What separations between the speakers give destructive interference? "M - t l f. What are the Ax/l ratios at the points of destructive interference? w ....m..umu.:-.:an.mmm... .. , Mama. Superposition - CHAPTER 21 21-9 ll. Two loudspeakers are shown at t = 0 8. Speaker 2 is #1 . B D 4mbeh1ndspeakerl. ‘_.4l l A C4‘ ‘8. x(m) a. Is the interference constructive or destructive? ,2 0 S a 'H #2 B . D 1 x lOA C4l T8I x(m) O b. What is the phase constant \$10 for wave 1? 7:( What is the phase constant ¢20 for wave 2? c. At points A, B, C, and D on the x-axis, what are: 0 The distances x1 and x2 to the two speakers? - The path length difference Ax = x2 — x] ? - The phases ab} and (p2 of the two waves at the point (not the phase constant)? 0 The phase difference Ad) 2 \$2 — (121? Point A is already ﬁlled in to illustrate. x1 X2 AX \$1 (152 A4) Point A l m 5 In 4 In 0.5% rad 2.521: rad 27rrad PointB Z W‘ (a w L! m 77’ TU“ TIT PointC 3 m 1L"? HM {'W 3'52”, Hr PointD H ’V‘ (‘W‘ L/W‘ Ur “T Z N d. Now speaker 2 is placed only 2 m behind speaker l. #1 Is the interference constructive or destructive? x . T . . - B o D i 1 l x (m) _4 A C 4 g I: O s l ‘#2 l . B ' D T l l x e. Repeat step c for the points A, B, C, and D. ‘4 0 A C 4 8 x1 X2 AX (P1 (P2 M) PointA M 3m 2w 05% WW «V Point B 2 M L‘ “4 2 "M 7” “V TT POintD H M Q “A 2 M bf 3 7], /( f. When the interference is constructive, what is AXI/l? What is A¢? M g. When the interference is destructive, what is Ax/l? What is Ag)? MT 7, m in f7 ru‘ E a. . 3 3 Superposition - CHAPTER 21 21-11 4 Q}, / 21.7 Interference in Two and Three Dimensions Key—m, gwymyﬂ. 14. This is a snapshot graph of two plane waves passing through a \x region of space. Each has a 2 mm amplitude. At each lettered point, what are the displacements of each wave and the net displacement? a.PointA:D1= 21”“ D2: ZW‘I‘“ Dnet: "lwm OWM b.PointB:D1= ZMM D2: ’1’” Dnet= 0. Point C: D1 = ’lw‘“ D2: ‘1“ Due; *‘W‘ 15. Speakers 1 and 2 are 12 m apart. Both emit identical triangular sound waves with A = 4 In and (1)0 = 7r/2 rad. Point A is r1 = 16 m from speaker I. a. What is distance r2 from speaker 2 to A? v-~,~———~-‘—" t: a. M 12m /.1:"l'<m‘>‘-+ WM} — 20"” b. Draw the wave from speaker 2 along the dashed line to just past point A. crest (weft d. What is the path length difference Ar = r2 — r1? _”l_WL What is the ratio Ar/ﬁt? ._l__ c. At A, is wave 1 a crest, trough, or zero? At A, is wave 2 a crest, trough, or zero? e. Is the interference at point A constructive, destructive, or in between? an Sf‘Y (A (\$14 16. Speakers 1 and 2 are 18 m apart. Both emit #1 4 m g m identical triangular sound waves with A = 4 m and (1)0 = 7r/2 rad. Point B is r1 = 24 m from speaker 1. 12m 16m 20m B a. What is distance r2 from speaker 2 to B? wmw a 7.-. ~- "0-1:" {(15va ‘+ (2%)“ 30m M b. Draw the wave from speaker 2 along the dashed line to just past point A. l . (N ' c. At B, is wave 1 a crest, trough, or zero? g . 1 At B, IS wave 2 a crest, trough, or zero? £1;— d. What is the path length difference Ar = r2 — r1? _(_0‘M_ What is the ratio Arl/l? ‘w'nt- : . . . I I f e. Is the interference at point B constructlve, destructlve, or 1n between? 6’65 W‘W ‘ ' i’ﬁ‘r'l.(_é, Superposition A CHAPTER 21 21-13 18. The ﬁgure shows the wave-front pattern emitted by two loudspeakers. a. Draw a dot c at points where there is constructive interference. These will be points where two crests overlap or two troughs overlap. b. Draw an open circle 0 at points where there is destructive interference. These will be points where a crest overlaps a trough. *2“ g ,_~ E \\ \ \a / -c ’1 ‘; a 1 v VD] Position along dotted line 60\lA b c. Use a hhlﬂeline to draw each “ray” of constructive interference. Use a-r-ed line to draw each “ray” of destructive interference. (1. Draw a graph on the axes above of the sound intensity you would hear if you walked along the horizontal dotted line. Use the same horizontal scale as the ﬁgure so that your graph lines up with the ﬁgure above it. e. Suppose the phase constant of speaker 2 is increased by 7: rad. Describe what will happen to the interference pattern. {PailWl/‘t WIN/owl {but-ill +9 #14 MM mﬂx Max/A44 ¥WWM ﬂ/afzf, ...
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## This note was uploaded on 08/25/2009 for the course PHY 213 taught by Professor Cao during the Summer '08 term at Kentucky.

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Interference_worksheet_key - _a‘_ Superposition - CHAPTER...

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