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9. Diagrams 9.1 and 9.2 show interference patterns using coherent sources of waves, λ.
Diagram 9.1 diagram 9.2
a (i) What is meant by coherent waves ? [1mark]
ii) Compare Diagrams 9.1 and 9.2.
Relate λ and x to make a deduction regarding the relationship of both quantities. [5 marks ]
b) Two loudspeakers placed 1.5 m apart are connected to an audio signal generator adjusted to a frequency 600 Hz.
When a student walks at a distance of 3.0 m in front of the loudspeakers he hears four consecutive loud and
3 soft sounds . Explain why? [ 4 marks ]
c) i) Explain why the wavefronts in the sea follow the shape of the coastline as the water becomes
shallower. [ 4 marks ]
To prevent similar damage in the future, the fishermen suggest building retaining walls and
relocating the jetty.
Make further suggestion of ways to help the fishermen solve their problems.
You should use your knowledge of reflection, refraction and diffraction of waves to explain these
suggestions, to include the following aspects. ( 6 marks)
(i) the design and structure of the retaining wall,
(ii) the location of the new jetty
(iii) the size or energy of the waves
d) Figure 9.3 shows the seashore of a fishing village. During the rainy season, waves are big. One year
the waves eroded the seashore, caused the jetty to collapse and damaged the fishermen’s boats.
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Fluid Dynamics Concepts Explained

  •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`a 6 b6 b c `a D@CV@F8?:AJF6J6F:@69D:6H `a 6 d e d d ec D@C@9K8FC8AJF6J6F:@69D:67 D@CV@F8?:AJF6J6F:@69D:6ef7
  •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
  •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`6E?43':;'EC4G'7''D;;38=:7'F==437' ' ' ' AQ' S==437':;'4@48=38';4@D' ' ' ' AR' Y4GG=784':;''E4=@'8:7D68=:3' ' ' ' AT' S:=47=@'D;;434784'83:GG'34GG=:3G'7'G434G' ' ' ' AW' 63347=';:3'34GG=:3G'7'F3@@4@' ' ' ' IX' BC74=8';4@D'F==437'D64'=:'4@48=38'863347=' ' ' ' I1' BC74=8';4@D'G=347C=V'aG:@47:Db' ' ' ' IA' BC7=6D4':;'EC74=8';:384' ' ' ' II' MF44D':;'3:==:7':;'7'4@48=38'E:=:3' ' ' ' IL' BC7=6D4':;'7D684D'4cEc;c'' ' ' ' IN' BC7=6D4':;'7D684D'863347='' ' ' ' IQ' ^348=:7':;'7D684D'863347='' ' ' ' IR' d6=F6='H:@=C4':;''=37G;:3E43' ' ' ' IT' _:G=':;'4@48=38'F:[43'=V3:6CV''8?@4' ' ' ' IW' d6=F6='H:@=C4':;'Dc8c'7D'c8c'C4743=:3' ' ' '
  • 4. !#$#%'()$*+,*(,$()#- . /(#')!!'#0-)! 1 2-*0#!!'#-(+#0!+-(34454 6 /!!#(+'(!)+78+#- 9,:'+8--##0-8*0(!)+78+#-77 ; ,,+#-+8--#(#-(!!#- = /!!#(+'?/ @ /!!#(+'(#0-)!#- A A BCDEACFGAHIJFKJHBLEM M BNOAPQARQSTUSRVW HXYZSUNVA[NT]S]Y IWVN]SPTZXSR CRRVSUN]SPTA^AZW . _:#`!'-!#,(:')# 1 _:#`!!+7,(:')# 6 _:#`!#0-7,(:')# a-+b,'+!-$(#' ))#8) ; 5#+#0-%')(#- = cd`!,(: @ a(!+(,`!b-+b, e f-+0)7!b-+b, g 2-8,,`!b-+b, . 2%,`!,(: .. a-!!8-,(: .1 0(-,!`!,(: .6 h$-!(,*(!,(: . a-+b,'+!-$(#' -*% .; i!#`!-*%j)(!! -,(#!0b .= ,,`!,(: .@ a-+b,'!8b-b!#' :($ .e 30)`!,(: .g 9(-(7(%`!,(: 1 k,(: M
  •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
  • 6. !#$%'()%(*%!+,$*%!$-. /012 345260782 9:;4=48274;0?42 @12 ABCDEFCGH IJK42L2MNL?=J=L=JK42KLON42PL4820?2LONOL=J0?207274L0?J?Q122 2 R12 STFCH IJK4274MNJ7482U2;4JVJ2J?V07WL=J0?22 2 X12 YZ[H 47JP42U2QJK424:;OL?L=J0?2U2W4=]082U0?8J=J0?2U2=4;2 0?47?J?Q2L?24K4?=2 2 ^12 _ZE`FaGH IJK42JWJOL7J=52L?828JVV474?42P4=644?2=602=]J?Q2 2 b12 YZ[HEcdTeH [TFCHDBHCTGHfFgcGH IJK42L2MNL?=J=L=JK42L?6472 2 h12 iDjjGaGkCDFCGH IJK42=]428JVV474?42U20?=7L=2P4=644?2=602072W0742=]J?Q2U2 4K4?=2 2 l12 STGkH m=L=42=]42=JW42072;47J082 2 n12 _ZkBCacdCH 7L628JLQ7LW2U20?42=]L=2N42Q40W4=7JLO2W4=]082U2=00O2 2 o12 iDBdcBBH IJK42KJ462V70W2KL7J0N2L;4=22 2 @p12qaZfGH m]062=7N=]2NJ?Q2WL=]4WL=JLO2W4=]082U24:LW;4O2U2VL=20V2 ;]5J2 2 @@12rcssGBCH IJK42L?2J84L2U20;J?J0?2 2 @R12tDkuH IJK42L?2L?64726J=]0N=2LONOL=J0?2U26J=]2JW;O42LONOL=J0?2 2 @X12_FgdcgFCGH IJK42L?6472=]70NQ]2LONOL=J0?2 2 @^12iGBdaDvGH w02=4OO2LP0N=20W4=]J?Q2x=0752OJy4z2J?284=LJO2L?825=4WL=JLOO5122 2 @b12{FvcgFCGH |77L?Q42=]J?QU8L=L2L078J?Q2=02;4JVJ482L;4=12 2 @h2A}`gFDkH IJK42W4=]08U74L0?2LP0N=20W4=]J?Q2J?2078472=]L=2J=2J24LJO52 N?847=008122 2 @l12_gFBBDj~HH m4;L7L=42J?=02L2V462Q70N;2L078J?Q2=02VJ:482]L7L=47J=J122 2 @n12uGkCDj~H €Jy20N=207284=47WJ?420W4=]J?Q2PL4820?2VL=U847J;=J0?2 QJK4?12 @o12rGCdTH 7L628JLQ7LWU;J=N74UQ7L;]2x?0=2L078J?Q2=02LO4z2 2
  • 7. !#$% '()*+%,)-, ./ 01234 56789:;%,;*6,*6%+=96:%6=:%6)=,6);,9-: 9-,+%;-+,6**%9-:+,*6?6-9-+69? .. @AB4 C9D%6,- .E F2GH4 C9D-6=+%9-?:#8%,+9-:,;*6, *)--+=)%*,,=9-,+%;-+ .I JK2KH4 C9D86*+,$9+;+()?6-6+9-=,;))%+ .L M1HNOPK4 C9D=,+6+8%*6,+8%,+9-:Q6,-86*+, .R SOTK4 U+6+86*+,=,+6+-+,9-)9-+8% .V W112XYH4 Z?6*6**%9-:+89(%% E[ 0HOXH4 C9D89-9+9-8%++%:9D- E/ 0HKH1GOXH4 ]9-6-,$%Q6,-)%*,,=%6,-9-: E. ^__`TK12KH44 C9D86*+,$9+,;))%+,;*6,96:%6,=%6,-,=()?6-6+9-+ 67*?6%6-96
  • 8. ! #$% $'( %) *+,-+./01023,+1)4-+4564-,+7-4 *+,-+./010234,-104- *1)4-+/430282942.,+02 : ;01023602+ 03= *+,-+./01023,+=03=4-+4564-,+7-4*+,-+. /010231,++4-,.+4-+/430282942.,+02 %)?.5,11 *7/.+,284+=,+-4@-,8+.103=+14..A !4@-,8+0B40294C 03=?1,-34 *7/.+,284+=,+-4@-,8+.103=+5-4 *5,11 ,.04-@-++,102+4-2,1-4@148+02+887-D E-0+08,1,2314 %,-34?/03 F0@@0871+@-++,102+4-2,1-4@148+02+887- %) %,-34?123@8,11423+=!4@-,8+103=+14..GH I)4-J@,142.K 03= *=-+@8,11423+=!4@-,8+103=+5-4 *=-+ 03=4-6)4-GG 8,11423+= %,-34?123 %)4-6)4- GL -4M7428NJ@ 4148+-5,324+),B4K 03= *=-+),B41423+= 03=6424+-,+026)4- GO P,B41423+=J@- 4148+-5,324+),B4K %23?1,-34 %)@-4M7428N %)6424+-,+026)4- GQ -4M7428NJ.729K 03= 03=60+8= *=-+),B41423+= *6-4,9.7+14.. %)?.5,11 ,B0231)4--4.0.+,284856,-49+)0-4. @+=4.,54+=08R24..,291423+=GS !4.0.+0B0+N 03=?1,-34 ,B023=03=4--4.0.+,284856,-49+)0-4. @+=4.,54+=08R24..,291423+= GT 45@@8411 %,-34?/03 *7661N,1,-34-87--42++=-73=+=4.,54 -4.0.+,284 G: I)4-J@4148+-08,1 94B084K 03=?1,-34 .4.5-4424-3N64-.4829 GA #1+,34J)-R023 B1+,34@4148+-08,1 94B084K 03= 449.,.5,114-87--42++6-9784,@0C49 ,572+@6)4-
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  • 11. 6 6 !#$#%#''()#*## -.# /!#('01#+#23'!#!4#54!#!4#+#16'7#!8'7#8189'#!1#:+)''#9(0# 5#!#'(##''.##/+#('01##4!16#!4#4!1639(#'#!#(8(;9.##B W.X /!#('01#+#23'!'#!4#!68(1'!7#'(#+#'69(1'#(5#5441'# ;0#+#,Y##5(,1(6'#.# B ].X ^'#5(,1(6'#!1#,1(8+'#0+Y1#''(1)#!#6(_#+#8!'#9(11.# B b.# :()#(!#!#+#6(1_'#(99!(5.##/+#6(1_'#3'3(99)#5('#+#36;1#!4# 8!'#12315.#B d.X e'01##(;9#4!16#4!1#'3,,'5#6!54(!'.#.,# # 3,,'5#6!54(!'# h89((!# iiiiiiiiiii.# iiiiiiiiii..# # # # Example: 9. Diagrams 9.1 and 9.2 show interference patterns using coherent sources of waves, λ. Diagram 9.1 diagram 9.2 a (i) What is meant by coherent waves ? [1mark] ii) Compare Diagrams 9.1 and 9.2. Relate λ and x to make a deduction regarding the relationship of both quantities. [5 marks ] b) Two loudspeakers placed 1.5 m apart are connected to an audio signal generator adjusted to a frequency 600 Hz. When a student walks at a distance of 3.0 m in front of the loudspeakers he hears four consecutive loud and 3 soft sounds . Explain why? [ 4 marks ] c) i) Explain why the wavefronts in the sea follow the shape of the coastline as the water becomes shallower. [ 4 marks ]
  • 12. To prevent similar damage in the future, the fishermen suggest building retaining walls and relocating the jetty. Make further suggestion of ways to help the fishermen solve their problems. You should use your knowledge of reflection, refraction and diffraction of waves to explain these suggestions, to include the following aspects. ( 6 marks) (i) the design and structure of the retaining wall, (ii) the location of the new jetty (iii) the size or energy of the waves d) Figure 9.3 shows the seashore of a fishing village. During the rainy season, waves are big. One year the waves eroded the seashore, caused the jetty to collapse and damaged the fishermen’s boats.
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