AL CE DSE. BY-TOPIC PAST PAPER .c: 0, ·- f I , 'i Ln lO U ,U DSE Physics - Section C : M.C. WAl : Wave Propagation PC-WAl-M/01 Part A : HKCE examination questions 1. 2. 3. p -------- Q - ----- R A transVerse wave is travelling steadily from left to right through a series of particles. At a certain instant the wave form is as shown in the figure. Which of the following statements about the particles is/are correct? (1) Particle P is IIlOVmg down. (2) Particle Q is moving up. (3) Particle R is momentarily at resL A. (I) only B. (2) only C. (1) & (2) only D. (2) & (3) only t = 0.000 s t = 0.025 s �--- �----· The above figures show a wave in the same section of string at two different instants, What is the greatest possible pe riod of the wave? A. 0.025 s B. 0.050s c. 0.100 s D. 0.200 s < HKCE 1988 Paper Il - 12 > �-� ------'----------�---------------- The above diagram shows a progressive transVerse wave at a certain instant when traVelling from left to right. 'Which of the following correctly shows the direction ofrootion of the particles at P, Q andR? A. B. C. D. p ➔ .j. -1- t Q ➔ -1- t -1- R ➔ -1- -1- t DSE Physics - Section C : M.C. WAl : Wave Propagation PC-WAl-M/02 4. < HKCE 1991 Paper ll- 23 > t � -----3>- Direction ofwave Vibrator A vibrator of frequency 5 Hz generates waves on a string. The above diagram shows the shape ofthe string at the instant when the vibrator has made one complete VJ.bration. Which of the following best shows the wavefon:n 0.1 slater? A. B. C. D. rJ\y- AAr � 5. < HK.CE 1991 Paper ll- 21 > 6. ---➔ Direction of wave p Q The above diagram shows a water wave travelling to the right. Which ofthe following statements is/are true? (1) PQ is equal to the wavelength. (2) PR represents the amplitude. (3) The particle at P will move to S after a quarter of a period. A. (1) only B. (3) only C. (1) & (2) only D. (2) & (3) only < HK.CE 1992 Paper II- 22 > A water wave travels towards the right. The above diagram shows the waveform at a certain instant. Which of the following statements is/are true? (1) Particle P is moving downwards. (2) Particle Q is moving upwards. (3) Particle R is momentarily at rest. A. (1) only B. (3) only C. (1) & (2) only D. (2) & (3) only DSE Physics - Section C : M.C. WAl : Wave Propagation PC-WAl-M/03 7. ---➔ Direction of wave £:\_____ D,__ Vibrator I P V Q A viorator generates a travelling wave on a string. The above diagnun shows the shape ofthe string at a certain instant Which ofthefollowing shows the shape of the string betweenPQ after a quarter ofa period? A R p Q c. D. (\} 8. < BKCE 1995 Paper Il- 24 > 9. Displacement/ cm 025 1--'\--/--\--�-+Time Is 0. --025 .2 0. .4 A train of water waves is generated in a ripple tank. The graph above shows the variation of the displacement of a cork placed in the water with time. Find the frequency of the waves. A. 0.2Hz B. 0.25 Hz c. 4Hz D. 5Hz < HKCE 1996 Paper II - 24 > X Direct;M � of t ----- ----- ----- Vibration --,. Direction of propagation Figurc(a) DWIJJacement Figure (b) A viOrator generates a travelling wave on a string. Figure (a) shows the shape of the string at a certain instant. Figure (b) shows the variation of the displacement of a certain particle on the string with time. Which of the following expressions represents the speed ofthe travelling wave? A. X B. y C. � y D. l'.. X DSE Physics - Section C : MC. WAl: Wave Propagation 10. < HKCE 1999 Paper II- 20 > PC-WAl-M/04 A cork in the water vibrates up and down 4 times in 2 s when a wave passes through it The distance between r.vo successive crests ofthe wave is IO cm. Find the speed ofthe water wave. A. 0.05mir 1 B. 0.1 ms-1 C. 0.2 ms- 1 D. 0.4ml> 1 11. < BKCE 1999 Paper II - 21 > The diagram shows a transverse wave travelling along a string. At the instant shown, particle Pis moving upwards. Which ofthe following statements is incorrect ? A. The wave is travelling towards the left. B. Particles P and Q VJ.lirate with the same :frequency. C. Particle Q is moving downwards at this :instant. D. Particle R is at rest at this instant 12- < HKCE 2{100 Paper II - 24 > Which of the following statements correctly descnbe(s) the meaning of the frequency ofa wave? (1) the time taken for the wave to make one complete vibration (2) the distance travelled by the wave in one second (3) the number of waves produced in one second A. (!) only B. (3) only C. (!) & (2) only D. (2) & (3) only 13. < HKCE 2001 Paper II- 23 > Direction of +---- wavem.otion R �::':',j�=k ,. ,�== = =��- ===== __,,,:;:�, = =--===== --========:=,=, Fo� corks are moving up and down on the surface of a pond as a water wave passes through them. At time t = 0, the positions of the corks are shown above. The figure below shows the displacement-time graph of one of the four corks. (Note: Displacement is positive when the cork is above the still vvater surface.) Di,p1",emont � L\ 0 V V J Time Which cork has the motion represented by the graph? A. p B. Q C. R D. S 14. < BKCE 2002 Paper II - 25 > A wave source generates waves of frequency 50 Hz. How long does it take for the waves to travel 100 m? A. 0.5 s B. 2s C. 5000 s D. It cannot be detennined as insufficient information is given. DSE Physics - Section C : M.C. WAl : Wave Propagation PC-WAl-M/05 Questions 15 and 16 : A transvezse wave travels along a string with a speed of 1.2 m s-1• The diagram below shows the shape of the string at a certain instant. Displacement/cm _____.,. Direction ofwave motion 15. 'Which ofthe following statements about the transverse wave are correct 'I (1) Its wavelength is 20 cm. (2) Itsfrequencyis 6Hz. (3) Its amplitude is 6 cm. A. (1) & (2) mtly B. (1) & (3) only C. (2) & (3) only D. (1). (2) & (3) 16. Which ofthe following diagrnn:,.s shows the shape ofthe string at a quarter of a period later ? A. B. --•' Displacement/cm Displacem<::=cm l-+--+----t-c--1-+--+--+Distance/cm ,1---+----'>--+--,-+Distance/cm 10 20 30 ., -3 ----- ----------- ----- C. Displacement/cm D. -3 ------------------------- 17. The solid curve in the diagram shows a transverse wave at a certain instant After 0.05 s, the wave has travelled a distance of 2 cm and is indicated by the dashed curve. Find the wavelength and frequency of the wave. Wavelength/ cm Frequency/ Hz A. 8 2.5 B. 8 5 c. 16 2.5 D. 16 5 Displacement/cm 3 ----- ----------- , , 2,m ., Questions 18 and 19 : DSE Physics - Section C : M.C. WAl: Wave Propagation PC-WAl-M/06 The displacement-distan.ce graphs of the particles along a travelling wave at time t= 0 and t = 0.2 s are shown below. Displacement at t = 0 "' Displacement at t = O 2 s \ ; I I -�i-- 0 I --1--i .+ 1--l-f l · 1-.J.�_J_,� -+- \-I· 1-:--: 1- ·I-H_J_1 I '-t-H-C -r-rLL.t .....L.LJ..�_J......L...L_I __ I LJ 2 18. < HK.CE 2005 Paper Il- 34 > Which of the following statements about the wave are correct ? (1) Its amplitude is 6 cm. (2) Its waveleng1h is 8 cm. (3) Its frequency is 5 Hz. A. (1) & (2) only B. (1) & (3) mtly C. (2) & (3) only D. (1), (2) & (3) 19. < HKCE 2005 Paper Il- 35 > 'What is the speed of the wave? A. 0.2ms-1 B. 0.3 m s- 1 C. 0.4ms-1 D. 0.Sms- 1 20. < BKCE 2006 Paper n- 16 > Distance In December 2004, an earthquake in the Indian Ocean caused a tsunami which produced water waves having wavelength about 100 m and frequency about 2 Hz. What was the approximate time taken for these water waves to trav el from the earthquake centre to Sri Lanka across a distance of about 1500 km? A. 1 hour B. 2hours C. 3 hours D. 4 hours DSE Physics - Section C : M.C. WAl : Wave Propagation 21. < HKCE 2007 Paper II -38 > PC-WAI -M/07 A longitudinal wave is travelling from left to right in a medium. Figure (a) shows the equilibrium. positions ofparticles A to J in the medium. At time t = 0, the positions of the particles are shown in Figure (b). Which of the following correctly shows the displacemenMime graph of particle I? (Note: displacement to the right is taken to be positive) A. 22. a h , ah , d direction of propagation d f g f h j k Figure (a) g hij k Fig,,re (b) Figirre (a) shows a series of particles which is uniformly distributed along a slinky spring. Figure (b) shows their positions at a certain instant when a travelling wave passes through the slinky spring from left to right Which of the following diagrams: shows the correct positions of the particles after half a period from the instant shown in Figure (b) ? ab, d ' A. a h ,d, B. a h ' C. h ' D. f H-4 : : ri- (4 f d,f g d g h g h ijk h e fgh i j j k DSE Physics - Section C : M.C. WAl : Wave Propagation PC-WAl-M/08 23. < HKCE 2009 Paper II - 36 > a h d e f g h j k 24. 25. Figure (a) Figure (b) Figure (a) shows a series ofparticles (a - k) at their equilibrium positions. Figure (b) shows the positions of the particles at a certain instant when a longitudinal wave travels to the right passes through the particles. Which are the directions of the motion of the particles c andf at the instant shown in Figure (b) ? particle c particle f A. to le.ft toleft B. to left to right C. to right to left D. to right to right < HKCE 2010 Paper II-34 > direction oftravel ---�------,quili'briumposition � wave trav� along a string to the left. The� abo� shows its waveform at time t = I s. 'Which of the following displa.cemenMime graphs best represents the motion of particle P ? (Take displacement upwards to be positive.) A. Displacement B. Displacement ti' 11, 6 2 4 ' 6 C. D. Displacement ti' ti' 6 5 6 < HKCE 2010 Paper IT� 35 > Figure (a) shows the equiliorium. positions of particles E to Nin a medium. A longitudinal wave is travelling from left to right. At time ti, the positions of the particles are shown in Figure (b). E F G H I J K L Figure (a) direction oftravel Which of the following particles is momentarily at rest at ti ? A. K B. L C. M equilibrium positions D. N Questions 26 and 27: DSE Physics - Section C : M.C. WAl : Wave Propagation PC-WAl-M/09 The figure below shows the displacement-distance graph of a wave travelling to the right with speed 2 cm s- 1 at a certain instant. P and Qare two particles at distances x = 8 <:m and 18 i:m respectively. Displacement/ cm ,p,___-___,,__4\J----+-PP-12\J _ l,__p_Q -.----2�------,,--• xi= 26. < HKCE 2011 Paper II- 34 > What is the period of the wave ? A. 0.25 s B. 4s C. 8s D. 18 s 27. What is the shortest tin,.e for p to have the same displacement as Q at the instant shown ? A. 1' B. 3s c. 4s D. 5s 28. < BKCE 2011 Paper Il- 36 > Figure (a) sbov,s a series of particles (E - 0) at their equihorium positions. Figure (b) sbo\W the positions of the particles at a certain instant when a longitudinal wave travelling to the right passes through the particles. Figure (a) � t _. , Figure (b) - Which of the following statements is incorrect ? A. The separation between F and N equals to the wavelength ofthe wave. B. The amplitude of the wave is4 cm. C. J is momentarily at rest at the instant shown in Figure (b ). D. N is at the centre of compression at the instant shown in Figure (b ). DSE Physics - Section C : M.C. WAl : Wave Propagation PC-WAl-M 110 Part B : HKAL examination questions 29. < HKAL 1992 Paper I- 20 > Fi gure (a) Figure (b) Figure (a) shows the etpmlbrium positions of equally spaced particles in a nwdium. A longitudinal wave travels from left to right through the medfum. At a certain inst.Int, the positions of the particles are shown in Figure (b). What will be the directions of.1I10tion of particle 1 and particle 7 at this instant 'l Particle 1 Particle 7 A. to the right B. to the right C. to the left D. to the left to the right to the left to the right to the left 30. < HKAL 1993 Paper I-24 > displacement 31. Ol�f-=;;'s----,f,Ll _.,, --,-,;,_---➔-. time in seconds �0.45 0.70"'-- A displacement-time graph of a particle in a travelling Wli'/e is shown. What is the frequency of this wave 'l A. 1.43 Hz B. 2.00Hz C. 2.22 Hz D. 4.00Hz < BKAL 1994 Paper IIA-14 > displacement/ m F LJ , position/m o o.,vo., o., Figure (a) dispIacement / m op '0;!_ /JL0J \_ • time I ms Figure(b) Figure (a) represents the displacement-position graph of a travelling wave at a certain instant and Figure (b) represents the displacement-time graph ofa particle in the wave. Calculate the speed of the wave. A 300m s· 1 B. 150ms· 1 C. 1.2m s· 1 D. 0.6m s·1 DSE Physics - Section C : M.C. WAl : Wave Propagation 32. < HK.AL 1995 Paper IIA - 12 > direction of propagation ofwave I I ! I I ! I 111 I I I 111 I A B PC-WAI-M/11 The above figure shows a longitudinal wave travelling to the right The particles 1 and B are .at the centre of a compression and a rarefaction respectivel y. Which of the following gives correctly the clirectJ.ons of motion of A and B at the moment shown? Particle A ParticleB A to the right to the left B. to the right at rest C. to the right to the right D. at rest to the right 33. B A C D The above figure shows a tnmsven;e wave propagating along a string. At the instant shown, the particle D on the string is moving downward. Which of the follow:ingdeductions is/are correct? (1) The wave is propagating to the left. (2) Particle B talces longer time to reach its equilibrium position than that ofparticle A. (3) Particles C and D are moving in opposite directions at the instant shown. A (!)only B. (3) only C. (1) & (2) only D. (2) & (3) only 34. < HKAL 2000 Paper IlA-17 > Displacement of air particles f---"�---c�/:______. ""�--- -, --- ➔) position +p -,,,---....__p - "J� The above figure shows the di sp lacement- position graph of a longitudinal wave at a certafu instant Take the displacement towards the right as positive, which of the following statements about particle Pat this instant are correct? (1) Pis a centre of compression. (2) P has the greatest kinetic energy. (3) Pis moving towards the right A. (1) & (2) only B. (I) & (3) only c. (2) & (3) only D. 0), (2) & (3) DSE Physics - Section C : M.C. WAI : Wave Propagation 35. < llKAL 2003 Paper IIA-14 > - ------� ----- PC-WAI-M/12 The figure shows three particles P, Q and R on a transverse wave travelling towards the right The three particles will reach their own equilibrium.positions at different times in the sequence of A. R,P,Q B. R,Q,P C. P,R,Q D. P,Q,R 36. Q I I l � x/cm 8 10 The above :figure shows the displacement y against the position x of a transverse wave travelling to the right at time t = 0. P and Qare two particles at x = I cm and x = 9 cm �ectively, Nex.t time when Preaches its crest position is at t = 03 s. Which of the following statements are correct? (1) The speedofthetransversewave is IO cms-1, (2) Particle Qfust reaches its crest position at t = 0.5 s. (3) When Qreaches its crest position,P also reaches its crest position. A (1) & (2) only B. (1) & (3) only C. (2) & (3) only D. (I), (2) & (3) Part C : BKDSE examination questions 37. The solid curve ill the above diagram shows a triltlsverse wave at a certain instant. After 0.05 s, the wave has travelled a distance of 2 cm and is indicated by the dashed curve. Find the wavelength and frequency of the wave. WaveJength / cm Frequency/ Hz A. 8 2.5 B. 16 2.5 C. 8 5 D. 16 5 2cm ,,--,, I', ' \\ ,/ / I \, \ ',.x / "Y, r---- I I \\ \ ,, :' / ' I/ DSE Physics - Section C : M.C. WAl : Wave Propagation 38. < BKDSE Sample Paper IA - 18 > direction of propagation -----�----- R PC-WAl-M/13 The figure shows the shape of a transVerse wave travelling along a string at a certain instant. Which statements about the motion of the particles P, Q andR on the string at this instant is correct 7 A. Particle P is moving downwards. B. Particle Q is stati.onaty. C. Particle R attains its maximum acceleration. D. p and Qare in phase. 39. 2 • • • • 2 4 4 5 6 • 6 7 • • 7 2= - 10 11 12 13 • • • • 9 101112 13 direction of propagation A longitudinal wave travels to the right through a medium containing a series of particles. The figure above shows the positions of the particles at a certain instant. The dotted lines indicate the equilibrium positions of the particles. Which of the following statements about the wave at the instant shown is/are correct 7 (1) The wavelength of the longitudinal wave is 16 cm. (2) Particles 8 and 10 are moving in the same direction. (3) Particle 3 is momentarily at rest A. (1) only B. (3) only C. (1) & (2) only D. (2) & (3) only 40. < BKDSE 2012 Paper IA-15 > abc d f ghijk •1tlilfflflifflm Fi-(a) a b c def g h i j ammoom1n11• Fi�•�) 5= A series of particles is uniformly distnbuted along a slinky spring initially. Figure (a) shows their positions at a certain instant wh en a travelling wave propagates along the slinky spring from left to right. Figure (b) shows their positions 0.1 s later. Wm.ch statement is correct? A. Particle e is always stationary. B. Particles a and i are in phase. C. The wavelength of the -wave is 16 cm. D. The frequency of the wave is 10 Hz. DSE Physics - Section C : M.C. WAl: Wave Propagation 41. < HKDSE 2013 Paper IA - 16 > displacement p direction oftravel - PC-WAl-M/14 The figure shows a snapshot of a section of a continuous transVerse wave travelling along the x-llirection at time t = 0. At t = 1.5 s, the particle Pjust passes the equilibrium position for a secondtime at that moment. Find the wave speed. A. 20 cms- 1 B. 12 cms- 1 C. 6cms~1 D. 4cms-1 42. Figure (1) ' , ' I-++ ,...,..,... . : t��+:+� : rt-, Figure (2) ,, ,+1 .. ..,.,. +: + � .,... :.· '..'. +! """!"a Figure (1) shows the equilibrium positions of particles a to k separated by 5 cm from each other in a medium. A longitudinal wave is travelling from left to right with a speed of 80 cm S- 1• At a certain instant, the positions of the particles are shown in Figure (2). Determine the amplitude and frequency of the wave. amplitude frequency A. '= 2 llz B. 6 = 4llz C. •= 2 llz D. 9om 4 llz 43. < HKDSE 2014 Paper IA-14 > direction oftravel -<------- p Q ---- ------- �------ s A transverse wave travels towards the left on a long string. P, Q, R and S are particles on the string. Which of the following statements correctly descnbe(s) their motions at the instant shown ? (1) Pis movingupwards. (2) Q and Sare moving in opposite directions. (3) R is momentarily at rest. A. (1) only B. (3) only C, (1) & (2) only D. (2) & (3) oruy DSE Physics - Section C : M.C. WAl : Wave Propagation 44. < HKDSE 2015 Paper IA - 12 > a b c de g h ab, d g a ' h PC-WAl-M/15 j Figure (a) k p;g,re (b) j Figure (c) A series of particles is uniformly distn'buted along a slinky spring initially. When a travelling wave propagates along the slinky spring from left to right, Figure (a) shows the positions of the particles at a certain instant Fi gur es (b) and (c) respectively show theirpositions 0.05 sand 0.1 slater. Which of the following is/are a possible frequency of the wave 7 (1) IO Hz (2) 20 Hz (3) 40 Hz A (1) only B. (2) only C. (3) only D. (!), (2) & (3) 45. < HKDSE 2016 Paper IA -15 > The above figure shows a snapshot of a transverse wave which travels along a string. Which statement is correct ? A. The wave is travelling to the left ifparticle P is moving upwards at this instant. B. Particles P and Rare moving in the same direction at thisinstant. C. Particle Q is at rest at this instant D. Particle R vibrates with an amplitude larger than that ofparticle Q. 46. Figure (a) shows the equilibrium positions of particles E to Nin a medium. At time t = 0, a longitudinal wave starts travelling fromkftto right At time t= l s, t he positions of the particles are shown in Figure (b). H J K L M N Figure(a) Figure(b) direction oftravel Which of the following statements MUST BE correct? ·h T ·;7 =!+"-: 'i-1- --i: equiltoriumpositions M N , , ' -\ - time= 1 s A. The distance between particles F and N is equal to the wavelength of the wave. B. The periodofthewaveis Is. C. Particle Eis always at rest D. Particle I is momentarily at rest at!"' I s. II DSE Physics - Section C : M.C. WAI: Wave Propagation PC-WAI -M/1611 47. SE 2018 Paper IA-15 > The figure below shows the displacement-time graph of particles P and Q on the same transverse travelling wave of wavelength A. displacement Q p \ y " I I\ 0 • 4 6 time/s \ \I I \ \ J\ , 1/\ Which ofthe following statements MUST BE correct? Upward displacement is taken to be positive. (1) At t ime t = 2 s, Pis mom.entarily at rest. (2) At time t = 4 s, Q is moving downwards. (3) The separation between the equilibrium positions ofP and Q is 0.25 ...t. A. (2)only B. (3) only c. (!) & (2) only D. (!) & (3) anly a. 49. Figure (1) shows the equilibrium positions of partidcs a to kin a medium. The particles are separated by 2 cm ftom each other. A longitudinal wave of frequency S Hz is travelling fi-om left to right. At a a:.rtain instant. the positions of the particles arc shown in Figure (2). Determine the amplitude and spec:4 of the wave. ' · am.pUtwle ,p«d A. 3.6c:m 40 cm.s w • B. 3.6an SOems-1 C. 2.4cm 40an s-• D. 2.4cm 80a:ns-l 50. The fi gure sbowi partoflhe m.,pt:accmcnt..distancc graph of a travelling wave of period Tat time t.., O, P is a pvticle on the waw. Which graph below con-ectly shows the 'VBriaf.ion of the particle's kinetic energy £ Within a period Ulmngihnnt•0'1 A. B. E T t T t C. D. :� L T t I DSE Physics - Section C : M.C. Solution WAl: Wave Propagation PC-WAl-MS/01 HKEAA's � Schenwis p.re9an:d fot the markers' tefcrence. It should not� regmled as a set ofxnodel � wee; Student, and teachers who are not involvedin the marking :PIQCCSS ate advised to intetpret the Marking Scheme with care. M.C. Answers I. D II. D 21. C 31. A 41. B 2. C 12. B 22. C 32. A 42. A 3. C 13. B 23. C 33. A 43. A 4. A 14. D 24. C 34. D 44. A 5. C 15. A 25. A 35. A 45. B 6. D 16. D 26. B 36. B 46. A 7. D 17. C 27. B 37. B 47. C 8. D 18. A 28. C 38. C 48. C 9. C 19. B 29. C 39. A 49, D IO. C 20, B 30. B 40. B 50. C M.C. Solution I. D ✓ ✓ 2. C R (1) Pis at the crest position, thus it nnist be momentarily at rest. (2) Draw the dotted line representing the wave at a later instant, Q is mov i ng up wards (3) R is at the trough position, thus it must be momentarily at rest In 0.025 s, the wa.vefonnpropagatcs by¾ ofits wavelength. :. Period= 0.025x4 = 0.1 s 3. C ilitection of wave motion - �--, ½7\:: _____ .,. __ ,._ _ _____�., .... -;----- ----�'-� -- 4. A T= ..!._ =_!_=0.2s f 5 DSE Physics - Section C : M.C. Solution WAl : Wave Propagation .-. AfterO.l s which is ± T, the wave should propagate by ½A.. 5. C ✓ ✓ P and Qare two particles in phase with mmimum separation ⇒ PQ = A Pis in ma:timuJl1 displacement ⇒ PR = amplitude PC-WAl-MS/02 (I) (2) (3) Particle P vibrates vertically about its equilibrium position, thusP will move to positionR. 6. D 7. 8. 9. ✓ ✓ D (I) (2) (3) R Pis at its maximum displacement and is momentarily at rest Q is moving upwards as shown by the above diagram R is at the instant of maximum. displacement and is momentarily at rest , ,,.(�\, ,,.T,\ ✓ I ' ;' : \ -�-�'-P.,: _.,__\.,-;-. "'""·:,r"---•:~Q�,�---- ' \ / ' ' ',./ \ After a quarter of a period, the wave would travel towards the right a distance of a quarter ofwavekngth. D From the graph, T"" 02 s. f•.!_• 2._ dHz T 0.2 C From figure (a), A"" x. Fromfi gur e(b), T'"'-y. v=f/4=!:.=3.. T y 11. 12. 13. 14. 15. C f• i,211z 2 DSE Physics · Section C : M.C. Solution WAl : Wave Propagation A.= 10cm = 0.lm .·. v = p. = (2)(0.1) = o.2m s-1 D ✓ ✓ ✓ B A B. C. D. P moves upward= the wave is travelling to the left All particles in same wave must have the same frequency Q is moving downwards at the instant shown R is moving downwards as shown by the above diagram PC-WAl-MS/03 (1) (2) (3) The time taken for the wave to make one complete vibration is the period. The distance travelled by the wave in one second is the speed . ✓ The number of waves produced in one second is the frequency. B p As shown in the above diagram, particles P, and R are momentarily at rest at t - 0 while Q is moving upwllids and S is moving downwards. Since the Displaccn:tent-tinw graph shows that the motion of cork is moving upwards at t = 0 :. Q is the answer. D Time taken should be found by t = d Iv. However, V = fi,, • As /. is unknmvn, v cannot be determined, so time taken to travel 100m cannot be determined. A ✓ ✓ (1) (2) (3) The distance that the wave repeats itself in 1 cycle is 20 cm. This is the wavelength. By v '°' f"J,. :. (1.2) = f (0.20) :. f = 6 Hz. The amplitude should be 3cm from the graph.. 16. 17. 18. 19. D DSE Physics · Section C : M.C. Solution WAl: Wave Propagation After a quarter of a period, the waveform should propagate ¼ wavel en gth towards the right. Thus the crest initially at 5 cm should move to the point at 1 O cm. C Wavelength: 'A, = 2 cm x 8 = 16 cm PC-WAl-MS /04 AI; the wave travels 2 cm, i.e. ½ 'A, in0.05 s which is ½ T, thus period T "" 0.05 s x 8 "" 0.40 s Frequency: f = ..!. = _l_ = 2.5 Hz A ✓ ✓ B (1) (2) (3) T 0.40 Amplitude is the maximum displacement, th us A = 3 x 2 cm = 6 cm Wavelength is the minimum distance to repeat itself; thus 'A, = 4 x 2 cm = g cm Since at t = 0.2 s, the wave has propagated ¾),,,,thus 0.2 s = ¾ T :. T = 0.267 s Frequency f = ..!. = _l_ = 3.75 Hz* 5 Hz T 0.267 v = E,_ = 3xz = 30cm.S-1 = 0.3m s-1 t 0.2 20. B 21. By v = f/2 By d = vt C Figure (a) Figure (b) displacement :. v = (2) (100) = 200ms-1 :. (1500 X 10 3 ) = (200) t O�__ypositinn Since the particle I is initially at the equilibri um position. t = 1500 s"' 2hours equ:ilil>tium position t = 0 displacement ofparticle I o��•- At a later time, it would move towards the left, i.e. it would have a negative displacement 22. 23. 24. 25. C DSE Physics - Section C : M.C. Solution WAl : Wave Propagation PC-WAl-MS/05 In Figure (b), particle ais at the centre of compression, thus it must be at the equihOrium position. After half a period, particle a shouldperform half a cycle, thus it must be still at the same equih'brium position but it then becomes at the centre of rarefaction. The graph in option C show s that particle a is at the rarefaction and at the same position, thus it is the answer. C Particle b andj are at the centre of compression and par ticlefts at the centre ofrarefaction. They are at the equilibrium positions. After a small time interval, the wave travels towards the right and is r epresented by the dotted line. Particle b and together with particle c nearby are moving towards the right Particle f is movin g towards the left. C tlirection oftravel �P ___ � "liibri .,. _'w ____ �--- ---------eqw umpos on The wave would travel towards the left after t = 1 s as shown by the dotted l ine. It shows that particleP is at the equilibrium position and is moving downwards at t = 1 s. Thus, option C shows the correcty - t graph for particle P. Note that position of Patt = I s. A E ; ' . , " direction oftravel time = ti From the graph, E and Mare at the centre of rarefaction and I is at the centre of compression. Centr e ofrarefaction and centre of compression must be at the equil ibrium pos itions and are moving at greatest speed. For a particle to be momentarily at rest, it must be at the extreme point, and its position should be at the middle of the compression and rarefaction. From the graph shown, particle Kis at the l eftmost position and must be momentarily at rest at !1. 26. 27. 28. 29. 30. 31. DSE Physics - Section C : M.C. Solution WAl: Wave Propagation B Wavelength: IL, = 8 cm By v - f' .·. (2) = /(8) Period: T= .!. = _l_ - 4, J 0.2s B :. f= 0.25Hz The wave is moving towards the right, thus particle P is moving downwards. PC-WAl-MS/06 To reach the position of Q, that is the crest, particle P has to move through ¼ cycle. Thus, the fune taken is f T. :.t=¾x4=3s C Particle Jis at the position of rarefaction, thus it must be at the equilibrium position. At equilibrium point, it must move with the maximum. speed, not at rest. Thus option C is incorrect. C Tak e the rightward direction as(+) : Particle I is moving towards the negative direction, thus it is moving to the left. Particle 7 is moving towards the positive direction, thus it is moving to the right B Period: T = 0.70- 0.20 = 0.5 s I=.!.= __1__ = 2Hz T 0.5 A From Figure (a), particles separated by0.6 mare in the same phase, thus the wavelength : IL,= 0.6 m From Figure (b), a partic le takes 2 ms to complete a cycle T=2xI0-3s J =}.. = -1- = sooHz T 2xI0- 3 V ""f/L, = (0.6) (500) = 300 m S- 1 32. 33. A DSE Physics - Section C : M.C. Solution WAl: Wave Propagation Take the rightward direction as(+) : Particle A is moving towards the positive direction, thus it is moving to the right. Particle Bis moving towards the negative direction, thus it is moving to the left. A ✓ (1) (2) (3) Particle D moves downward ⇒ the wave moves to the left A moves upward before going downward but Bmoves downwatd only ⇒ A : takes a longer path to reach the equih'britunposition C and D both move downward. PC-WAl-MS/07 34. D ✓ (1) Pis a centre of compression 35. 36. ✓ ✓ A (2) (3) since the particles at the left hand side of P have positive displacement, i.e. moves to the right ; while the particles at the right hand side ofP moves to the left. P:atequihl>riumposition ⇒ maximumKE p: has(+) displacement later ⇒ moving to the right Af. the installt shown, particle P is momentarily atrest, particle Q and R are moviog downwards. Time for P to reach the equilibrium point = ¼ T Time for Q to reach the equih"briu!n point > ¼ T Time for R to reach the equihnrium point < ¼ T B ✓ ✓ (2) (3) At this instant, P is moving downwards. As it takes 0.3 s for P to reach the crest position that performs ¾ cycle, the period is 0.4 s. Wavelcngth ofthewaveis4cm. Speed= ;\,IT= {4)/(0.4)=10cm s-1 At t"" 0.5 s, Q should reach its trough position. The separation of P and Q is two wavelengths, thus their motions are in phase. 37. 38. 39. 40. B DSE Physics - Section C : M.C. Solution WAl : Wave Propagation PC-WAl-MS /08 Wavelength: /1. = 2 cm x 8 = 16 cm As the wave travels 2 cm, i.e. ½ /1. in 0.05 s which is ½ T, Period T = 0.05 s x 8 = 0.40 s Frequency : f = l = _l_ = 2.5 Hz T 0.40 OR As the wave travels 2 cm in 0.05 s, speed: v = !!.. = � = 40 cm. s-1 By V = JA C • A. ✓ A B. C. D. rightwards """""' :. (40) = I (16) t 0.05 :. f= 2.5Hz M P is at the crest, it must be momentarily at rest. M Q is at the equilibrium position, it must have the maximwn speed and must be moving. MR is at the extreme position, its acceleration is the.maximum. M the separation between P and Q are not n A, they cannot be in phase. 2 3 4 5 ��: • 4 5 6 7 1 � .. .. _ .... ---: • 6 7 10 11 12 13 ,, .... .... : -.,.--��L ,__ �� ..� : • • • • 10 11 12 13 Draw the displacement- position graph as shown in the above figure. Note that particles 3 and 11 are at the compression and particle 7 is at the rarefaction. ✓ (1) • (2)' • (3) B • A. ✓ B. • c. • D. The separation between two compressions is 1 wavelength. :. A = 8 x 2= 16 cm After a short time, the wavewould move rightwards to the dotted position. Thus, particle 8 is moving leftwards and particle 10 is moving rightwards. They are moving in opposite directions. Particle 3 is at the equilibrium position, it must have the maximum speed, but not at rest For a travelling wave, particles maybe momentarily at resl There is no particle that is always atresl In Figure (a), particles a and/ are both at the compression, thus they are in phase. The separation between a and i is one wavelength, which is 32 cm.. Particle a is at the compression in Figure (a) and at the rarefaction in Figure (b), that is, particle a has moved through half cycle of the oscillation, thus the time taken is half period. tr=0.ls .·. T=0.ls :.f=liT=1!0.2=5Hz DSE Physics - Section C : M.C. Solution WAl : Wave Propagation PC-WAl-MS/09 41. B From the graph, wavelength: /2 = 30 - 6 = 24 cm In 1.5s, particle P performs ¾ cycle, thus it talces a time of¾ T, where Tis the period. :. T = 2s Frequency: f = ..!.. = .!. = 0.5 Hz T 2 Speed : v = f J. = (0.5) (24) - 12 cm s- 1 42. A 43. From Figure (2), particles b andj are at the centres of compression. Separation between them is the wavelength. :. /4 = 8x5 = 40cm Byv = fli ;. (80) - /(40) ;. f- 2Hz From Figure (2), as particle bis at the compression andparticle/is at the rarefaction, they are at eqnilibriwn positions. Particle d should then be at the extreme position. Displacement ofparticle dis the arnplitude. .-. Amplitude = 6 c m A After a while, the wave would shift to the left shown as the dotted Cl,lt'l'e. ✓ (!) (2) (3) Particle P is moving upwards. Particles Q and S should move in the same direction. Particle R is not momentarily at rest, but mo ving downwards. 44. A In Figure (a), particle e is at the centre of compression. ✓ (!) (2) (3) fff= lOHz,then T= I.=..!__= 0.1s. Afteratirneof0.05s: t = �T= fT, / 10 U particle e should travel ½ cycle to the position of the centre of rarefaction as shown in Figur e (b). Thus,f= 10HzispossiOJe. Iff= 20Hz,th en T= _!_= 2.. = 0.05s. Afteratimeof0.05s: t =IT, / 20 p article e should travel I cycle to the position of the centre of compression, but not the rarefaction as shown in Figure (b). Thus,/= 20 Hz is imp ossible. If f= 40Hz, then T= _!_ = 2.. = 0.025s. Afteratimeof0.05 s: t = 2 T, / 40 particle e should travel 2 cycles to the position of the centre of compression, but not the rarefac tion as shown in Figure (b). Thus,/= 40 Hz is impossible. 45. B • A ✓ B. • C. • D. 46. A ✓ A. • B. • c. • D. 47. C ✓ (!) ✓ (2) • (3) DSE Physics - Section C : M.C. Solution WAl : Wave Propagation PC-WAl-MS/10 Ifparticle Pis moving upwards, the wave should be travelling to the right Ifthe wave is moving to the right, then bothP andR are moving u.pwards. Ifthe wave is moving to the left, then both P and R are moving downwards. Thus, they must be m oving in the same direction at this instant Particle Q is at the equilibrium position 1hat bas the greatest speed, it must be moving. Particle Rand Q should be moving with the same amplitude since it ls a travelling wave. From Figure (b), bothE and Mare at the centre of rarefaction, thus distance between E and Mis one wavelength. Therefore, distance between the next particles, F and N, is also one wavelength. There is no information concerning the period or frequency of the wave. In a travelling wave, there is no particle that is always at r est. Particle I is at the centre of compression, it is moving towards the right at this instant. At t = 2 s, P is at the position of trough, thus it must be moinentarily at rest A t t = 4 s, Q is at equilibrium positon and later at a lower position, thus it must be moving downwards. P and Q are neither in phase nor anti�phase,, there is no phase relation oonceming tbcir separation. DSE Physics - Section C : Question WAl : Wave Propagation Part A : HKCE examination questions 1. < RKCE 1981 Paper I - 6 > PC-WAl-Q/01 A transverse wave is travelling steadily from left to right through a series of particles. At a certain�� vnve fonn is as shown in the above figure. Each ofth.e vt'bratingparticles is observed to perform four complete oscillatLons m 16 s. (a) Find the following quantities: (i) the amplitude of the wave, (u) the wavelength. (iii) the period, (iv) the frequency. (b) At the instant shown, which of the particles P, Q, R, S, T is/are (i) moving upwards, (il) moving downwards, (iii) momentarily at rest? (c) What will be the position of particle Q a qtlazter of a period later 'I (5 marks) DSE Physics - Section C : Question WAl : Wave Propagation 2. PC-WA1-Q /02 A vertical vibrator generates waves on a string. It takes 0.25 s to produce a complete wave of wavelength 0.8 m on the string. (a) Find the frequency and speed oftbe waves on the string. (b) How longdoes it take for the wave to propagate a distance of2 m ? (2roarks) (c) The figure below shows the shape of the string at the instant vrl1en the vtDrator has made one complete vibration. Direction of t Vibration ,J, � Directionofwavemotion D I- 0.Sm ----J.j (i) At the instant shown, whlch ofthe particles A, B ,. C, Dis/ are (1) moving downwards, (2) at rest? (2marks) (ii) Sketch the shape ofthe string after 0.125 s. In your figure sh.ow the positions of the particles A, B, C andD. (4nurrks) DSE Physics - Section C : Question WAl : Wave Propagation PC-WAl-Q/03 3. Figure I '. ;; , , ..i..11..tt:L1.1...1..Li. .:J .. J�i.·d:H:r2 _ ,_l-i£B A Iongitidi.nal wave is travelling from left to right in a medium. Figure 1 shows the equilibriuDl po_sitions_ of some particles A to Kin the medium. Figure 2 shows the positions of the particles at a certain time t when the wave 1s passmg through them. (a) What is meant by a longitudinal wave? Give an example of a longitudinal wave. (b) Point out a particle in Figure 2 which is (l) at the centre ofa comp ression, (ii) at the centre ofa rarefaction. (2 marks) (2m&ks) {c) The table below shows the displacements of particles A and B at time t. (Note : Displacement to the right is taken to be positive.) (i) Using Figures 1 and 2, :find the displacements of the other particles and complete the Table below. (2 maxks) (nj In the figare below, draw a graph showing the displacements of the particlesalongthewave at tune t. · (2 marks) ' _, -10 Displacement/cm ' J¼tf·' \-J� -i , ·cr-i-,rrc, f DSE Physics - Section C : Question WAl : Wave Propagation 3. (c) (iii) Find the amplitude and wavelength of the wave. {iv) If each particle takes 0.25 s to complete one oscillation, find the speed of the wave. 4. < HKCE 2002 Paper I - 4 > Q PC-WAl-Q/041 (2-k,) p ----------· Equilibriuznposition 0.3m ---- A wave is generated on a string. The figure above shows the shape of the string at a certain instant At this instant, both particles P and Qare moving downwards. (a) State the type ofwave generated on the above string. (I :mark) (b) What is the direction of1l:aveI of the above wave? (l=k) (c) At the instan.t shown, which particle (P or Q) has a greater speed? Explain briefly. (2mawJ (d) Find the wavelength of the wave. (1 DWk) (e) Describe the motions ofparticlesP and Q at a quarter of a period later. (2 maw) DSE Physics - Section C : Question Solution WAl : Wave Propagation PC-WAl-QS/01 HICEAA's Matking Scheme is� for the ntarkets' xefert:nce. It should not be regarded as a set of model answers. Students and tcacheis who ate not mVolved in the marlting process are advised to inte;rJltet the Matking Scheme with care. Question Solution I. 2. (a) (i) A= 2cm (ii) 'A.= 8cm (iii) T=4s (iv) f = 025 Hz (b) (i) R,S (u) P,T (ili) Q (,) Q is at 2 cmbelow its present position (a) Frequency = 4 Hz Speed=!!._""� = 3.2ms-1 t 025 (b) By d = vt _-. (2) a (3.2) I t = 0.625 s (,) (i) (1) A (2) BandD (u) D OR _______!: -------- ----------- v=f/2=4x0.8=3.2ms- 1 < For wave fon:n > < 0.5 mark for each particle> 3. (a) A longitudinal wave is a wave in which the 'Vibrations are parallel to the direction of travel of the wave. Example: (Any ONE of the following) * Sound waves * Ultrasonic waves * Waves generated in a slinky spring (b) (i) ParticleA (OR J) i satacentreofcompression. (u) Particle Eis at a centre of rarefaction. [l] [l] [l] [l] [2] [2] [l] [2] [l] [2] [l] [l] [2] [2] [1] [l] [l] [l] 3. (c) (i) (ii) DSE Physics - Section C : Question Solution WAl : Wave Propagation Particle C D E F G H I Displacement/ cm -8 -6 0 6 8 6 0 -5 PC-WAl-QS/02 [2] J K -6 -8 _10 'iti: 1 =1==:TF;./:0, t:r+.-·-i��ti#.Jfflt:+=l::¥ +1 · + · . 4. (a) (b) (,) (d) (e) < Correct points > < Correct curve > (iii) Amplitude = 8 cm Wavelength = 80 cm (iv) speed = /A, a -1-x0.8 "'3.2mS-l 0.25 It is a transverse wave The direction is towards the left. ParticleP has a greater speed, since it is at theequiblmum position. Wavelength= o 3 = 0.2 m 1.5 Particle P is momentarily at rest. Particle Q is moving downwards. [l] [l] [!] [l] [1] [l] [1] [l] [l] [l] [l

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HKDSE Physics Elective C Wave Motion by topic

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