Waves Past Paper PDF

TOPIC WAVES AS PER P MC SYLLABUS Learning Obiectives: i. Define and apply the following terms to the wave model; medium, displacement, amplitude, period, comp...

TOPIC WAVES AS PER P MC SYLLABUS Learning Obiectives: i. Define and apply the following terms to the wave model; medium, displacement, amplitude, period, compression, rarefaction, crest, trough, wavelength, velocity. ii. Solve problems using the equation: v =f. i. Describe that energy is transferreddue to a progressive wave. iv. Compare transverse and longitudinalwaves. V. Explain that speed of sound depends on the properties of medium in which it propagates and describe Newton's formula of speed of waves. vi. Describe the Laplace correction in Newton's formula for speed of sound in air. vii. Identifythe factorson which speed of sound in air depends. vii. Describe the principleof šuper position oftwo waves from coherent sources. ix. Describe the phenomenon of interferenceof sound waves. X. Describe the meaning of wave motion as illustrated by vibrations in ropes and springs. xi. Demonsträte that mechanical waves require a medium for their propagation while electromagnetic waves do not. xi. Explain the formation of stationarywaves using graphical method xiii. Define the terms, node and antinodes. xiv. Describe modes of vibration of strings. XV. Describe formation of stationarywaves in vibrating air columns. xvi. Explain the principle of Superposition xvi. Explain S.H.M and explain the characteristics ofS.H.M. TOPIC4 Waves Wavess Wave is a disturbance produced in a medium by which energy is transferred from one point to another point by the vibration of particles of medium. Waves transport energy and momentum without transporting mater (mass). Wave Production: For production of waves in a medium, few parameters are required, as: 1.Elasticity 2.Restoring Force 3. Inertia Production of waves always require medium, whether they need itfor propagation or not. Classifiction of Waves MechanicalWaves (Require medium Electromagnetic Waves Matter Or De-broglie Waves for Propagation) (Mcdium does not required (Associated witlh the for propagation) motion of charged particles) Radio Waves Example: Cathode rays Micro Waves Infrared Radiation Shock Waves Progrevsive Waves Visible Shock wave, strong pressure wave in any Anae., which transfers Ultraviolet energy by moving away elastic medium such X-rays as air, water, ora from the souree of solid disturbance, is called a Y -rayS subxtance, produced by progressive or traveling supersonic aircraft. Wavc. explosions, lightning, or other phenomena that ereate iolent changes DO YOU KNOW? in pressure. Usually Longitudinal. produced during: Volcanic Eruption Transverse Particles Waves vibrales perpendicular to Longitudinal Particles Waves vibrates through transverse all waves can medium waves can pass but pass. SonicBoom parallel to direction direction of through only solid medium. of waves propagation Earth Quake waves propagation The transverse wave consists of crests and troughs. Crest: The portion of the wave above its equilibrium position (mean position) is called crest. Crest Direction of travel Amplitud Equilibrium position Wavelength Trough Direction of disturbance Trough: The portionof thewave below its equilibrium (mean) position called trouph. Wavelength: Ihedistance between any two consecutive crests or troughs js the same ulong the length of the ope. is called the wavelength and is denoted by 2. t t Head Ottsce STARS ENTRY TEST SERIES IoaeLatiore  TOPIG-4 Waves Wave Spced: The speed of the wave can be measured by timing the motion of a wave crest over a measure distance. The speed of a periodic wave can be found from its frequency and wavelength. V=for v= because f = 1 T Same medium (Air or Vacuum) Different medium (any other than air or vacuum) If two waves are travelling same in If twowaves are travelling in any other medium then medium then both waves will have same both waves will have same frequency that they had speed. Wave with greaterfrequency will before entering that medium. Wave with greater have smaller wavelength. wavelength will have greater speed. V=Constant f=constant 1 Intensity of a wave: The intensity lof the wave is directly proportional to the square of its amplitude & frequency. Ic A DO YOUKNOW? max (A,+A,) |Amplitude is the ratio of maximum speed tóangular (A,-A,)' mun frequency. | MCQ.I The diagram below represents the variation with time of pressure at a point in air through which a sound wave is travelling at340 ms. AD/ Pa 100 200 300 400 N0limo/s -25 What is the frequency of the wave? A. 1.7Hz B. 5.0 x 10 Hz C. 1.0 x 10Hz D. 3.1x 10 Hz Solution: Period of the sound wave., T=200 us 1 Frequency of thewave =T 200x10 -5kHz or 5.0x 10' Hz. Reflection of Transversc Waves: Ifa transverse wave traveling in a rarer medium is incidenton a denser medium. it is retlcete of 180° (r radian). such that it undergoes a phase change in a denser medium isincident on a rarer medium. Ifa trarisverse wave traveling it is reflccted without any change in phase. Sound: wave A vibrating body produces sOund waves, It is type of mechanical Sound waves are longitudinal waves having three-dimensionalpropagation in air. and rarefactions. Longitudinalsound waves consist of compressions ot particles of medium is minium Rarefactionís region where crowding  A Sound waves Interference but not polarization produce Reflection, Refraction, Diffraction, because sound waves are longitudinal. Compression is a region where medium is maximum. crowding of partcles of Alr Molecules Amplitude Wavelengh The diagram shows a water BRAINSTORMING wave in a ripple tank. 3.0 cm O 15cm 1.5 cm The wave has a speed of 12 cm/s at R. The wave crossesa boundary PQ where What is the velocity of the wave at the distance between crests changes from 3.0cm to 1.5 cm. A. 3.0 cm/s point S? B.6.0 cm/s C. 12 cm/s D. 24 cm/s WAVE EM waves SPEED (s) 3x108 Sound in air at 20CO Sound in water 343 Sound in steel 1500 Glass 5000 Rubber 4540 Intensity of sound: 60 Sound intensity is defined asthe sound power per unit area. The usual of sound intensity in the air at a listener's location. The basic context is the measurement The most common units are approach to sound intensity measurement is to wattsm² or watts use the decibel soale: cm. Im=10log.o Speed of Sound in a Medium Newton's Formula: Newton proved that when longitudinal waves (sound) medium, it depends on rmove in elastic Compressibility of the medium Inertia Where E the modulus is of elasticity of the medium andp is its density. TEST SERIES Head STARS ENTRY OffRce: 36harTown I Lahore S4  TOPIC-4 Eor Solids: Modulus of elasticity Waves E= Young's modulus of elasticity =Y V= For liquids: Modulus of elasticity E Bulk modulus elasticity of =K y= For gases: For a gaseous medium. Newton assumed that the propagation of longitudinal wave is an isothermal process(temperatureremains constant). In this case, modulus of elasticity E= Pressure of the gas =P P V= Note: Wave velocity in a medium is fixed. Wave velocity is a material constant. It does not depend on wavelength, frequency and intensity. Newton's Formula for the Speed of Sound in Air: The speed of sound waves depends upon the density and elasticity of the medium. The lighter the medium,the more quicklywill the sound move form point to point in the medium. Newton assumed that sound travels through air adiabatically and hence Newton's formula for the speed of sound is given by At standard temperatureand pressure, we have P=latmospheric pressure = 101325 N/m? p=1.29 Kgm T= 0°C By putting these value in above fermula we have, v= 280.22 ms at 0°C But, the experimentalvalue of speed of sound in air at0°C 332 ms!. Thus, the theoretical value is is about 16% less than the experimental value. This error was corrected by Laplace and is known as Laplace's Correction: Laplace' pointed out that Newton's assumption was wrong. Since compression and rarfactions occurs so rapidly that there is no transfer of heat, hence propagation of sound through air is adiabatic process. Laplace assumed that sound travels throughair adiabatically and got the formula as: v= As p= 1.29 kgm,P= 101325 Nim', y= 1.42 (Forair) Putting these values in above formula,we get V= 333 ms- at0°C,this value is very close to the experimental value ects on the Speed of Sound in a Gas: Efect of pressure: Withthechange of pressure, the velocity of soundin a gas remains unchanged, IS, there is no effect of pressure on the velocity of sound in gas, Jiect of temperature: T.Thus, the sound is directly tothe e Velocity absolute of sound c temperature, 1.e, velocity of proportional Square root of STARS jENTRY rTEST SERIES Head Office Johar Towh Lahore  V273+t Effcct of V= v, + 0.61t humidity: With the decrease in density of the medium the velocity of sound inereases.The moist air he dry air. Therefore,the velocity of sound in moist air is more than the is lighterthe velocity ofsound in dry air. Pmoist air Pary air V moist air Y dy air Audible Frequency Range Sourd also exhibits the phenomenon of total internal reflection Sound travels longer as exhibited by light. distance at nightthan The sound waves in during day. are audible to the frequengy range human ear. Sound waves 20Hz 20,000 Hz - For Your Information below 20Hz are called infrasonic waves while Frequencies those above 20,000 Organisms ultrasonic waves. Hz are called (Hz) Ultrasonic waves are not ear. These are audible to human Dolphin 150– 150,000 produced naturally by avoiding collisions with bts and help it in Bat 1000 120,000 - obstacles while flying. Cat JThe sound in a 60-70,000 building or immediately alter the auditorium does not die Dog 15-50,000 source has ceased to Human continues for produce it. It 20-20,000 some-time because of the source has multiple reflections. ceased to emit waves is This persistence of called reverberation. audible sound after INFRA SONIC SOUND) Sound waves having SONIC frequency Sound waves less then 20Hz are called having frequency ULTRASONIC range between Sound infrasonic waves. 20Hz. waves having 20000Hz arecalled and more than frequency These waves with very faint sonicwaves. 20000Hz are called This is sound are heard by animals audible ultrasonic waves. just of humans. frequency range before earthquake. Ultrasonic waves are used in Principle of medical field and to Superposition: find depth of When two or more than sea or two waves undergroundobjects. then total displacement at pass a any point is equal particular point in a This is called principle of to the sum medium simultaneously superposition" of the Thus if the particle of the displacements of allthe waves. medium is displacement due to each of the simultaneously acted individual n upon by n displacementofthe particle dueto n waves be waves such that its wavesis yi, y2, Interference of Sound: yy+yr..+ yn *.yn then the resultant Superposition(mixing up) of two identical propagating along same direction Îs called sound waves their while Tynes Interference: passing of interference. through same mediutm 1. Constructive Interference If the two waves meet at a point in same interferernce is called constructive phase, such that the interference two waves help Hence. each Other. such compression of | STARS ENTRY TEST SERIES Head Ofcei fohar T one wvave falls on the  compression of the other wave and rarefaction of one wave falls on the rarefaction of other wave. The intensity of resultant sound increases which in tun increases the loudness ofthe sound. 2. Destructive Interference Ifthe two waves meet at a point in opposite phase, the two waves cancel each othet's effect. This type of interference is called destructiveinterference.In this case, compression of one wave falls on rarefaction of other wave. As a result, the intensity of resultant sound decreases which inturn decreases the loudness of sound. constructive interference destructive interference AA+ AA vAAA. (a) (b) Conditions for interference for interference of sound: Sound sources must be coherent same frequency Sound waves must travel in the same medium with Sound sources must be close to each other that the sound waves reinforce each other, so In constructive interference,two interfering resultant is a louder sound. interference Echoing zone is region of constructive Silence zone is region ofdestructiveinterference of paths traveled by two waves in reaching the Path difference is the difference between lengths same point. Construetive interferenee Destruetive interference Parameters Path difference n where n=1,2,3,4,5.... (2n +) where n=1,2,3,4,5. 2n (2n +1) Phase difference where n=1.2,3.4,5.... where n=1,2,3,4,5..., Amplitude A,gu =A,+A, Ane =A,-A, Intensity MCQ.1 The ratioof velocity of sound in air at 4 atmosphere and that at 1atmosphere pressure would be: B.4:1 1:1 A. C.1:4 3:1 D. Solution: not affected by change of pressure alone. Velocity of sound in MCO. Find thetenmperature atwhich the velocity of sound in air ls two times its velocity at 10°C. B. 859K A. 1132°C  Solution: POINTTO THE PONDER T, =n'T the string fixed at one end only I, =2x 283 If and theother end is free, then No.of nodes =No.ofantinodes T, =1132K or 859°C Stationary Waves or Standing Waves: When two similar waves move along the same line in a medium but in opposite directions, these Waves will combine according tothe principle of superposition and form waves called stationary Waves. incoming wavc reflected wave reflecting surface Antinode Antinode Wave formed by the Node Node Node incoming and reflected wave 'combined'wave a short time later reflecting Wavelength ). surface In stationary waves there are some points which shows permanently known as nodes. zero displacement are And the points which have maximum amplitude called Anti- POINT TOTHE PONDER nodes. The distance between two consecutive nodes or antinodes is A When a string fixed at both ends vibrates into 'n' loops, 2 then = No. of nodes N=n+1 The distance between a node and the next antinode is = No. of antinodes A=n 4 The points between the two successive nodes are in phase with each other The nodes always remain at rest, S0 energy cannot flow pass these points. Hence ctanding in the medium energy between nodes, although it alternatesbetween potential kinetic forms. and When the antinodes are all their extreme displacements theenergy stored is wholly potential and when they passing through their equilibrium positions, the energy is wholly kinetic energy. Organ Pipe: 6An organ pipe is a wind instrument n whien sound is produced due to setting up of in air column". stationary waves.neistsof a long tube in which air 1s rorced rom one end and sound is produced by means of air column. This forced wave is reflected from the other end vibrating travels back and interferes stationary waves,. with the incident wave to produce POINT TO THEPONDER Organ pipe isof two types; The pipe open at both endsis richer () Open organ pipe In harmonic than that of a pipe (i)Closed organ pipe closed atone end.  "If one end an Consider a string of length'whichAn organ pipe that is open at both of organ pipe is ends is caled open organ pipe closed it is called closed organ pipe." ends kept stretched by clamping its is Since air is free to vibrate at an open The particles air at a closed end sothat the tension in the string of is F cannot move and hence closed end f we pluck the string at its middlena, we mus get an anti-node at the always node. noint, the string vibrates in one loop open end So, the stationary waves of pipe is which set up in an open pipe, must be as shown in the Figure. Such that they have an antinodes at Distance betweentwo nodes= length both ends. of the string I modeof vibration A closed pipe emits fundamental 36, no other frequency when there is end I modeof vibration node in between an antinode Minimum number of nodes in end. If A is the betweentwo successive antinodes is and nodal one. If 4 is the wavelength of sound wavelength of soundthen produced by pipe. Ist mode of sibratinn Then or,-21 4 4 2 or 2 A=21 Iff is the frequency of vibration The speedv of the waves in the sting then depends upon the tension F of the Here, 1- length of pipe V string and m (mass per unit length) of Iff is frequency, then f,=V f= the sting, it isgiven by F is called fundamental This m frequencY. As v =fÀ,and A=21 V Rnd mode of vibration Iffi isfrequency, then In this mode of vibration there may be one node in between an for antinode end and nodal end. This is the expression Ifsbe the wavelength of sound fundamental frequency in an open f is frequencywith which the lowest pipe. then in a a transverse wave is produced Cud mode of sibration string and is called fundamental Inthis mode of vibration, there may frequency be two nodes in betweenthe 2 4 4 Rnd mode of vibration are antinodes at the two ends, Ifa is In this mode of vibration, there OR A, three nodes and two antinodes in the wavelength of sound set up then If6 be frequencyof vibration then 'stretched string. 3v 2 2 2 or 1 IfGis the frequency of vibrations Iff is the frequeney of vibrations then, then, 6-3f: This is frst overtone or third harmonie. This is called first overtone or second harmonic. In this emodeof vibration there 6-26 may be two nodesin betweenan This is called first overtone or rd mnle ol vibraton antinode end anda nodal end. IfÀ econd hermonle In this mode of vibration, there are isthe wavelength of sound then Tour nodes and threoe antinodes in In this mode of vibrations there ane stretched string.  21 three nodes in between the two 2 2 2 2 ends. Ifs is the wavelength of sound,then 2 2 4 4 Ifff is frequency of 3F vibration then, 41 or f,-Y3v 4 2 2 4 2 5 =3f, 21 \m 21 20 Iff is the frequency of vibration This is called or then second overtone or 3 third harmonic. V V Iff is frequency of vibration then, Conclusion 2 n V V 20/ 20 3v OR 5 f; 5f, 41 /3 ny n F OR f,-3 This is second overtoneor fifth 2,, 21 21 Vm nf, This is called second overtone or harmonic. Thus,when a closed pipe is Where n= 1,2, 3, 4...... (rich third harmonic. sounded,various frequencies Conelusion harmonics) emitted by it are fi. 3f,. Sfi... No. of nodes 21 Conclusion N=H+1 2 n 41 No. of nodes=Harmonic no. + 1 nv No, of Antinodes f,= >f,=nf, 4 n 21 nv A=H No. of Antinodes-Harmonic no. where n 1,2, No. 3..(rich of nodes harmonics) f, =nf,41 N=H where n = 1,3, 5... (odd No. of nodes-Harmonicno. harmonics) No. of Antinodes No. of nodes A=H+1 H+1 No. N= of antinodes=Harmonic no.+1 2 No.of Antinodes H+1 A=. 2 iis known as fundamental frequency while other frequencies are known as overtone. MCQ.J A stringwith linear mass density m= 5.00 x 10"kg/m is under a tension of 80.0N. What will be the speed of the wave produced in the string? A. 10 ms-! B. 20 ms! D. 40 ms C. 30 ms Solution: T 80,0N 40.0ms! 5.00x 10kg/m MCQ.2 steel wire is 1 m and the fundamental frequency is 250 Hz, of the The length of a stretched the velocity in it is: transverse wave B. 250 ms A. 125 ms 1000 C. 500 ms! D. ms Solution: v=fa, ,2m V 250x2500 ms  DO YOU KNOW HOW TOCALCULATE HARMONIC NO. FROM OVERTONE? STRETCHED STRING OPEN AT BOTH ENDS OPEN AT ONE END Harmonic =Overtone +1 Harmonic =Overtone +l Harmonic =2(Overtone)+1 MCQ3 The fundamental frequency of opcn-end organ pipe is fo. Its new fundamental frequency when half flled with water is: A. f B. 2 D. 2 3 Solution: When thepipe is half filled with water, it becomes a closed pipe with length 24 i=2l same wavelength existed in open pipe. Therefore, frequency remains unchanged Understanding S.H.M. Simple harmonic motion is a type of periodic vibratory motion in which to instantaneous displacement & it is always directed towards mean Acceleration is directly proportional position Le c -Xa motion is periodic vibratory motion. Hence a ssystem is said to be executing S.H.M if its should also have DO YOU KNOW? It Inertia > Elasticity Spring constant K has same Restoring force unit as surfacetension. Some Basic Concepts: motion & } To fro motion about a fixed point called vibratory intervals of time periodic if it repeats itself afterregular Oscillatory motion iscalled two-dimensional or three-dimensional Vibratory motion cab be one-dimensional, F = Kx force directly propotional to extension wvithin elastic limit According to Hook's law is Where K spring constant (its S.Iunit is Nm) direction brings back the vibrating body towardsmean position. Its is Restoring force is a force which alwavs towards mean position. i.e F, --Kx FOR YOUR INFORMATION 0 -Qmas 0 P.Emas equilibrium iitb) 7 -Vmas clmax K.Emax 0 P.Enas 2 fc) 3T 0 T'may K.Ema P.EmaN el Hodd Orfee na TioLahore 61 STARSIENTECTEST SERES  Fest -Fext -F. Amplitude is the. maximum displacement from mean position it is usually denoted by x, Do Vou Know: Instantaneous displacement is the displacement of Spring constant is also known as the vibrating body from mean position at any stiffness constantor force constant. instant.It is usually denoted by x. Spring constant depends upon: One complete round trip of a vibrating 1. Radius and length of the wire. body is called a vibration 2. Material of the wire. In one complete vibration, a body 3. Unstretched length thespring. covers a distance of equal to 4-times of its amplitude. (S=1Vib=4A) In one complete vibration,displacement covered willbe zero. Time to complete one vibration called time period. Its S.I unit is second. Frequency is the number of vibrations per second. its S.I unit is Hz (1Hz =s)..f= 1 T > Angular frequency is given by o-.T Its S.l unit is rad s! COMBINATIONS OFSTRINGS Series Combination ParallelCombination Iftwo springs are combined end to end Iftwo springs are combined Side by side (Series)then equivalent spring constant will (Parallel)then equivalent spring constant will be equal be equal to: to: 111 ke k, k, k In case of two springs with In case of two springs with same same spring Keg constant: spring constant: k2k In case of 'n' springs with same spring In case of 'n'springs with constant: samespring constant: kea kmin n -k-nk of springs, Force In parallel combination In series combination ofsprings, Force acts remains same but spring show different differentlyon springs but spring show same extensions. extensions. keqf Observer Case: 2 If an observer is moving with speed uo away from a seneratingasound stationary source of speed v.then the change in apparent frequency Hence f'