eP11

heinemann

units1

&2

Physics

Carmel Fry

Rob Chapman

Keith Burrows

Doug Bail

Geoff MillarHenry Gersh

112n

ded

itio

n

CHAPTER 1 The Nature of Waves 21.1 Introducing waves 3

1.2 Representing wave features 10

1.3 Waves and wave interactions 18

Chapter Review 25

CHAPTER 2 Two Models for Light 272.1 Modelling simple light properties 28

2.2 Refraction of light 36

2.3 Applications of refraction 48

2.4 Light described as an electromagnetic wave 56

2.5 Dispersion and polarisation of light waves 65

Chapter Review 70

CHAPTER 3 Mirrors, Lenses and Optical Systems 713.1 Geometrical optics and plane mirrors 72

3.2 Applications of curved mirrors: concave mirrors 76

3.3 Convex mirrors 84

3.4 Refraction and lenses 91

3.5 Concave lenses 97

3.6 Optical systems 102

Chapter Review 112

Area of Study ReviewWave-like Properties of Light 113

CHAPTER 4 Nuclear and Radioactivity Physics 1184.1 Atoms, isotopes and radioisotopes 119

4.2 Radioactivity and how it is detected 124

4.3 Properties of alpha, beta and gamma radiation 131

4.4 Half-life and activity of radioisotopes 136

4.5 Radiation dose and its effect on humans 142

Chapter Review 147

Area of Study Review Nuclear and Radioactivity Physics 149

CHAPTER 5 Aspects of Motion 1525.1 Describing motion in a straight line 153

5.2 Graphing motion: position, velocity and acceleration 164

5.3 Equations of motion 172

5.4 Vertical motion under gravity 176

Chapter Review 181

ContentsINTRODUCTION V

WAVE-LIKE PROPERTIES OF LIGHT

NUCLEAR AND RADIOACTIVITY PHYSICS

MOVEMENT

CHAPTER 6 Newtons Laws of Motion 1836.1 Force as a vector 184

6.2 Newtons first law of motion 191

6.3 Newtons second law of motion 196

6.4 Newtons third law of motion 204

Chapter Review 213

CHAPTER 7 Work, Energy, Power and Momentum 2157.1 Work 216

7.2 Mechanical energy 222

7.3 Energy transformation and power 231

7.4 The relationship between momentum and force 239

7.5 Conservation of momentum 248

Chapter Review 252

Area of Study ReviewMovement 253

CHAPTER 8 Concepts in Electricity 2588.1 Electric charge 259

8.2 Electric forces and fields 266

8.3 Electric current, EMF and electrical potential 272

8.4 Resistance, ohmic and non-ohmic conductors 280

8.5 Electrical energy and power 288

Chapter Review 295

CHAPTER 9 Electric Circuits 2979.1 Simple electric circuits 298

9.2 Circuit elements in parallel 304

9.3 Cells, batteries and other sources of EMF 309

9.4 Household electricity 317

Chapter Review 322

Area of Study ReviewElectricity 324

APPENDIX A 328

APPENDIX B 330

SOLUTIONS 331

GLOSSARY 343

INDEX 348

ELECTRICITY

Heinemann Physics 11 is the first book in the exciting series, Heinemann Physics,

written specifically for the VCE syllabus at years 11 and 12.

First and foremost in the minds of the authors has been a desire to write a text

that will support students learning in physics while making the subject interesting,

enjoyable and meaningful. The book has been written using clear and concise

language throughout, and all concepts have been fully explored first in general and

then illustrated in context. Much care has been taken to use illustrative material

that is fresh, varied and appealing to a wide range of students of both sexes.

The book boasts many features that will help students and teachers find it easy

to use. Each of the books nine chapters has been divided into a number of self-

contained sections. At the end of each section is a set homework-style questions

that are designed to reinforce the main points. Further, more demanding questions

are included at the end of the chapter. These could be used for assignment or

tutorial work. A further set of exam-style questions is included to cover each Area

of Study. These could be used for revision. There are over 1000 questions in the text

and all answers are supplied.

Within each section, the concept development and worked examples occupy

the main 2/3rd column. The remaining 1/3rd column has been set aside for some

of the 600 photographs and diagrams, as well as small snippets of interesting

Physics File information. The longer pieces of high-interest and context material

are contained in the full-page-width Physics in Action sections. Both Physics in

Action and Physics Files are clearly distinguishable from other material.

HEINEMANN PHYSICS 11 SECOND EDITION

The second edition of Heinemann Physics 11 has been fully revised and upgraded

to match the content and focus of Units 1 and 2 of the 2004 VCE Physics Study

Design. Any section which contains background or extension material outside the

syllabus is contained under a section heading in a non-shaded banner.

The new edition is presented as a student pack consisting of textbook

and ePhysics 11 student CD. Successful features of the first edition

have been retained while improvements in design and presentation

will make the book even easier and more stimulating to use.

Heinemann ePhysics 11 features a complete electronic copy of

the textbook plus all Detailed Studies. Each Detailed Study is a self-

contained unit of work, structured to ensure efficient and effective

coverage of the chosen topic. A major innovation is the inclusion of

Interactive Tutorials that model and simulate key physics concepts.

Cross references in the textbook to these and Practical Activities

suggest when it is most appropriate to undertake these new activities.

Introduction

Introduction v

See Heinemann ePhysics CD for an Interactive Tutorial

PRACTICAL ACTIVITY 9Reflection in a plane mirror

Detailed Studies

Heinemann Physics 11 second edition Support Material:

Heinemann Physics 11 Teachers Resource and Assessment Disk

makes planning, structuring and implementing the new syllabus easy.

It contains PhysicsBank 11, an electronic database of questions and worked

solutions, a wide range of innovative and accessible practical activities and Sample

Assessment Tasks, which teachers can use directly or modify. A detailed course

outline and work program is also included.

vi PHYSICS 11

DOUG BAIL

Is an experienced physics educator and writer with a particular interest in thedevelopment and integration of new technologies into science teaching. He hasbeen Head of Science and Agriculture at Tintern Anglican Girls Grammar Schooland maintains a passion for making physics relevant, stimulating and accessible toall students. He led the development of the new Practical Activities which form partof the teacher support material. These activities were extensively trialedthroughout Australia and include a range of activities from teacher demonstrationto discovery-based investigation suiting a range of learning styles and needs. Thisincludes many short activities for when time is limited!

KEITH BURROWS

Has been teaching senior physics in Victorian schools for many years. He is amember of the Australian Institute of Physics Victorian Education Committee andwas actively involved with the VCAA in the design of the new course. Keith was aVCAA representative involved in introducing the new VCE course to physicsteachers in Victoria and running workshop sessions for teachers. He is particularlykeen to portray The Big Picture of physics to students. Keith would like toacknowledge Maurizio Toscano of the Melbourne University Astrophysics Groupwho has provided invaluable help and advice in the preparation of the Astronomyand Astrophysics detailed studies.

ROB CHAPMAN

Has taught physics for over twenty years and has been keen to explore thepossibilities presented by changing technologies over the years. He has beenScience Coordinator at St Columbas College in Essendon where he wasinstrumental in introducing the use of datalogging technology to junior scienceand senior physics classes. Rob is currently teaching Senior Physics at PEGS(Penleigh and Essendon Grammar School). He has written a wide variety ofcurriculum support material including physics units for the CSFII. Rob has alsoproduced physics trial examination papers and is the author of the acclaimedPhysics 12A student guide.

CARMEL FRY

Has 14 years involvement in development of text, CD and on-line curriculummaterials for VCE physics. She is Senior Teacher and co-coordinator of SeniorPhysics at Eltham College of Education where she is currently managing theintegration of IT into physics education. Carmel is the author of numerous textsand multimedia resources. She was a VCAA representative involved in introducingthe new VCE course to physics teachers in Victoria and running workshop sessionsfor teachers.

Carmel has led the development of the Interactive Tutorials which are anexciting innovation on the student CD.

Newtons laws of motion vii

About the Authors

HENRY GERSH

Has taught physics and mathematics in a wide variety of courses at TAFE collegesand universities. He has led the development of the PhysicsBank utilising his vastexperience in question creation and the writing of clear but detailed workedsolutions.

GEOFFREY MILLAR

Has had 26 years experience teaching science and senior physics in two states. Hehas been very involved in the development of good curriculum, methodology andpractice in physics, and has a continuing interest in the subject. He was Director ofCurriculum at Geelong College for seven years.

REVIEW PANEL

Principal reviewer/consultant Dr Colin Gauld has taught mathematics and physicsat secondary schools and science method to prospective science teachers at theUniversity of New South Wales. At present he is a Visiting Fellow in the School ofEducation at the University of New South Wales. The teacher review panelconsisted of experienced VCE physics teachers and physics educators. The authorsand publisher would like to thank the following people for their input: Dr BarbaraMoss, David Jagger, Martin Mahy, Dr Maurizio Toscano, Peter Kolsch, VincentVignuoli, Lyndon Webb and Catie Morrison.

AcknowledgmentsThe publishers wish to thank the following organisations who kindly gavepermission to reproduce copyright material in this book:

AAP, pp. 159, 192 (left)ANT Photo Library, p. 312Australian Picture Library, pp. 66, 139, 160(all), 168 (right), 184 (a), 201, 257Keith Burrows, pp. 280Coo-ee Picture Library, pp. 45 (right), 184 (c)Malcolm Cross, pp. 23 (both right), 63 (both), 76 (right), 88, 213 (all), 249Dale Mann, p. 268 (all)Mark Fergus, pp. 36 (both), 77, 97, 102, 184 (bottom), 282 (both)NASA, pp. 71, 192 (right)Newspix, p. 155PASCO Scientific p. 161(right)Photodisc, pp. 1, 2, 4 (left), 8 (both), 15, 20, 27, 29, 31, 50, 133, 140, 158, 173, 184 (d),196, 222 (top), 229, 232 (top, centre and bottom right), 300Photolibrary.com, pp. 3, 4 (right), 22, 45 (left), 72, 109, 118, 122, 124 (both), 129(bottom), 142, 183Rainbow, p. 146 RMIT/Craig Mills, pp. 37 (both), 233Sport:The Library, pp. 151, 153 (both), 168 (left), 184 (b), 185, 209, 225 (both), 236, 241The Age, p. 169The Picture Source/Terry Oakley, pp. 23 (left)Tom Taylor, Tmation, p. 293Victoria Police Traffic Office, p. 174Every effort has been made to trace and acknowledge copyright material. The author and publisher would welcome any information from people whobelieve they own copyright material in this book.

viii PHYSICS 11

What benefit could there be in knowingmore about light? Well, everyoneknows about the common benefitsthat come from our ability to manipulate thepath of light. For hundreds of years we havebeen able to magnify small objects with micro-scopes and look into the distance with tele-scopes. Spectacles have helped people witheye defects to see their world in sharp focus.Today our ability to deal with the wave-likeproperties of light means that enormousreflecting telescopes collect weak light signalsfrom space and optical fibres carry our com-munications across the world. In this area ofstudy you will learn just how these devices workand develop an insight into the nature of lightitself.

Our knowledge of light in this technologicalage means that humans now produce more light

than at any other time in history. Since we relylargely on incandescent and fluorescent light-ing, every bit of light energy produced meansthat considerable heat is simultaneously pro-duced, and the implications of heating ourworld are well accepted. Fortunately quantumphysics tells us that there is a better way toproduce light. The electrons in an atom give outa flash of light whenever they jump from a highenergy level to a low one. Small electronicdevices called light emitting diodes (LEDs) usethis effect, but for a long time they couldnt beused to make light that was similar to sunlight.But the technology is approaching. LEDs indevelopment may mean that besides beingabout 20 times more efficient than currentlight globes, they give off no heat and last a life-time. You never need to burn your fingerschanging a light bulb again!

WAVE-LIKE PROPERTIES OF LIGHT

you will have covered material

from the study of the wave-like

properties of light including:

an explanation of the role of

conceptual modelling used by

scientists to explain

phenomena

how waves involve the transfer

of energy without the transfer

of matter

the differences between

transverse waves and

longitudinal waves

how to represent waves

how to define waves by their

amplitude, wavelength, period

and frequency

the speed of travel of waves

the relationship between the

velocity, frequency and

wavelength of a wave.

CHAPTER 1

BY THE END OF THIS CHAPTER

The nature of waves

Would you know what was coming if you were sitting on apicturesque beach in Hawaii and suddenly the coastalwater in front of you seemed to retract before your eyes,leaving the tethered fishing boats sitting on beds of sand? You mayhave enough knowledge of coastal waves to realise that the waterat the shore was being dragged back to help to build a gianttsunami way out to sea. Tsunami is the Japanese term for thephenomenon that used to be called a tidal wave. Since its nothingto do with the tide the name tidal wave is being dropped.Regardless of what youd call it, you would be advised to get tohigh ground, and quickly!

The ability to forewarn the affected coastal people of theoccurrence of a tsunami anywhere in the world would undoubtedlysave lives. Appropriately, it may well be our knowledge of adifferent category of wavesgravity wavesthat someday allowsus to do this. Gravity waves are not just any ordinary type of wave.Albert Einstein in his general theory of relativity predicted theirexistence early last century. General relativity treats the Universeas a four-dimensional surface called spacetime. Gravitationalwaves are the curvature of spacetime caused by the motion ofmatter. If a gravity wave arrived at Earth it would cyclically shrinkand stretch the dimensions of everything around us, but by suchminiscule amounts that even the strongest gravity waves arenearly impossible to detect.

Einsteins general theory of relativity was the same theory thatsuccessfully predicted the bending of the path of light by thegravitational fields of massive objects. It was not until the 1970sthat strong experimental evidence for the existence ofgravitational waves in space was found, though they havent beendetected here on Earth yet. Aside from showing us where theblack holes, supernovae, etc. are located throughout theUniverse, the detection of gravity waves should tell us all aboutthe big bang and break down our limits regarding how far intospace we can see. Along the way Australian gravity physicistshave invented a device that can accurately monitor coastal oceanwaves and provide warnings of potentially life-threatening swells.We too will focus our attention on the water as we begin our ownstudy of the nature of waves.

The nature of waves 3

Figure 1.1 If we can learn enough aboutthe properties of waves we can address thequestion Does light have a wave nature?.

Why combine the study of waves and light?The first part of your course involves a study of the wave nature of light. As youembark on this study you will be walking in the footsteps of many famousphysicists from the past, who were devoted to the quest of revealing the truenature of light. In the following chapters the question as to whether light hasa wave nature is addressed. Before such a discussion can begin, we must havean understanding of the nature of waves themselves! Like the physicists thatpreceded us we will study the waves that can be seen on the surface of waterand the waves that can be made to travel along springs and strings. Throughthis examination we will be able to describe how waves behave and collate alisting of the properties of waves. In particular, we will be looking for the rulesof behaviour that seem to be true for waves alone, and not for othermechanisms of motion. Once we have put together the rules describing thebehaviour of waves the question as to whether light has a wave nature can beaddressed.

You may have recognised that our quest is really just a quest to find asatisfactory model for the behaviour of light. Scientists rely heavily on modelswhen they attempt to explain all kinds of phenomena. If an unknown ormysterious entity or observation can be linked with something with which weare familiar, then we can get closer to understanding it. For example, in theearly 1900s physicists described the unknown structure of the atom bymodelling it on the familiar structure of the Solar System. They depicted theorbits of electrons around the nucleus as comparable to the orbits of theplanets around the Sun. This was a most useful model at the time and althoughnot completely accurate, it set the scene for future progress regarding ourknowledge of the atom.

If waves are to be our chosen model for light then they must appear tobehave largely in the same manner as light does. That is, if a wave model forlight is to be accepted then it will need to be able to explain the knownbehaviours of light. A very successful model would illustrate all of thebehaviours of light. Perfect modelling is rare in science. Rather it is more likelythat we make use of the insight that a particular model provides and, as wasthe case with our early models of the atom, use it as a stepping-stone tofurthering our understanding.

Waves transfer energySometimes it is really obvious that energy is being transferred. A golf club hitsa golf ball and the ball flies through the air, or the water stored in a dam isreleased, making a turbine spin, or a volcano erupts suddenly spurting out hotlava and heating the surrounding region. In all of these cases energy istransferred from one location to another. Later in the course we look at theconcept of energy in detail and study its various forms. For the moment,simply appreciate that energy is an abstract idea. An understanding that itallows work to be done and items to be moved around is sufficient.

There is another manner in which energy can be transferred from onelocation to another. This mechanism does not involve a single body carryingthe energy with it from its origin to its final location, but rather the energy is

1.1 Introducing waves

Australia has joined the quest to detectgravity waves with the commencement ofconstruction of the AustralianInternational Gravitational Observatory(AIGO) just north of Perth, WesternAustralia. This facility will use tiny changesin the path of laser light to detect theelusive gravity waves.

Physics file

Check out the InteractiveTutorial, The Wave Equations.

4 WAVE-LIKE PROPERTIES OF LIGHT

Any time we observe energy to have been transferred from one location toanother by the passing of the energy from one particle to the next within asubstance we say that a mechanical wave has been created. The substancecarrying the wave is called the medium. Note that in order to pass on the wavethe particles within the medium each temporarily possess some (kinetic) energyand pass it along to the adjacent particle through physically vibrating againstit. As the wave energy passes through, each individual particle of the mediumwill not have any overall change in its position. This is why a floating piece ofdriftwood will be observed to merely bob up and down as waves pass by.

Later we will see that mechanical waves are not the only category of wavesthat exist. Radio waves and microwaves, for example, also transfer energy fromone place to another without a net transfer of matter. There are many wavesthat can carry energy without requiring a medium. Some of these are visitedlater in the course. Remember that our objective is to gain an understandingof the general properties of waves. We shall focus our attention on the tangibleand readily observed mechanical waves that can be seen to travel in water,springs and strings.

carried through the particles of a substance. A dramatic example of this is atsunamia huge ocean wave created when there is a movement in the Earthscrust under the sea. The energy created at the location of the shift in the crustis passed along by the particles of the ocean water at speeds of around800 km h1, and can reach the coastline in the form of a towering water wavethat causes devastation. None of the water particles that flow onto the shorewill have been originally located near the source of the tsunami. Only theenergy has been passed along.

All WAVES involve the transfer of energy without a net transfer of matter.

Figure 1.2 (a) Particles carry energy as they move, this energy can be transferredto another item as it collides with it. (b) Waves carry energy through a mediumwithout the need for an item to have travelled from the source to the receiver.

PRACTICAL ACTIVITY 1Disturbance and propagationof a disturbance

(a) (b)


Mechanical wavesA mechanical wave involves the passing of a vibration through an elasticmedium. Energy must be present at the source of the wave and this energy isdescribed as being carried by the wave. Overall the medium itself is notdisplaced. Examples of mechanical waves include the vibrations in the earththat we call an earthquake, the sound waves emitted by a speaker, and thedisturbance that travels along a guitar string when it is plucked.

A model of an elastic medium is shown in Figure 1.3. Balls joined togetherby springs represent the particles of an elastic medium. Each particleoccupies its own mean (average) position. An initial disturbance of the firstparticle to the right will result in energy being passed along from particle toparticle. The particles are not all disturbed at the same time; rather thedisturbance gradually passes from one particle to the next. Also note that, forexample, as particle 2 pushes against particle 3, particle 3 will push back onparticle 2. Hence particle 2 is returned to its mean position after it has playedits role in passing on the energy. Ideally all of the energy that was presentinitially will be passed right through the medium. In practice, the temperatureof a medium will increase ever so slightly due to their movement.

Wave pulses and continuous wavesWhen a single disturbance is passed through a medium in the mannerdiscussed we say that a wave pulse has occurred. Each particle involved incarrying the energy is displaced once as the pulse passes through, and then theparticles gradually oscillate back to their mean positions. Many examples ofwave motion, however, involve more than one initial disturbance or pulse at the origin. Continuous waves are created when there is a repetitive motionor oscillation at the wave source. Energy is carried away from the source in theform of a continuous wave. A vibrating speaker producing sound waves in

1 2 3 4 5

Figure 1.3 This model of an elastic medium helps us to envisage the passage ofmechanical waves through a medium.

wave pulse(a)

(b)

one initial disturbance

continuous vibration at source

Figure 1.4 (a) A single wave pulse can be sent along a slinky spring. (b) A continuously vibrating source can establish a periodic wave.

PRACTICAL ACTIVITY 2Waves in a slinky

air forms a continuous wave, for example. When a medium is carrying acontinuous wave the particles of the medium will vibrate about their meanposition in a regular, repetitive manner. These are also called periodic wavesas the motion of the particles repeats itself after a particular period of time.

Transverse and longitudinal wavesSince all waves carry energy, for any wave the direction of travel of energy canbe considered. There are two clearly different categories of mechanical waves.Longitudinal waves involve particles of the medium vibrating parallel to thedirection of travel of the energy. An example of this is shown in Figure 1.5a. Asthe operator vibrates his hand in a line parallel to the axis of the spring, alongitudinal pulse is created. The particles of the medium (or the windings ofthe spring in this case) will vibrate in the direction shown. The vibrations areparallel to the direction of travel of the wave. Sound waves are a commonexample of longitudinal waves. When a speaker cone vibrates it causes nearbyair molecules to vibrate as shown in Figure 1.5b and this is parallel to thedirection in which the sound energy is sent.

Transverse waves are created when the direction of the vibration of theparticle of the medium is 90 (perpendicular) to the direction of travel of thewave energy itself. Figure 1.4a shows an example of how this could beachieved. As the operator shakes her hand in a direction perpendicular to theaxis of the spring, a transverse disturbance is created. Each particle of themedium will be moved as a pulse passes through. The particles each vibratearound their mean position, but this vibration is perpendicular to thedirection that the energy is travelling in.


(a)

(b)

vibration of source

vibration of source

vibration of medium

next pulse created

wave energy

wave energy

vibration of air molecule

speaker

1.

2.

3.

4.

Figure 1.5 (a) When the vibratory motion and the direction of travel of the wave energy are parallel to one another, a longitudinal wave hasbeen created. (b) Sound waves are longitudinal waves since the molecules of the medium (air molecules) vibrate in the direction of travel of energy

Water waves are often classified astransverse waves but this is anapproximation. If you looked carefully at acork bobbing about in gentle water wavesyou would notice that it doesnt movestraight up and down but that it has amore elliptical motion. It moves up anddown, and very slightly forward andbackward as each wave passes. However,since this second aspect of the motion isso subtle, in most circumstances it isadequate to treat water waves as if theywere purely transverse waves.

Physics file

PRACTICAL ACTIVITY 3Waves in a rope

Sources of one-, two- and three-dimensionalwavesAnother convenient classification system for waves considers the number ofdimensions that the wave energy travels in. One-dimensional waves occurwhen longitudinal or transverse waves are sent along a spring or rope. Theenergy travels along the length of the conducting medium.

Two-dimensional waves allow energy to be spread in two dimensions.Waves travelling across surfaces are two-dimensional. Ripples travellingoutward across the waters surface when a stone is dropped into a pond is a


PHYSICS IN ACTION

If you dont have a slinky spring handy youcan still get the idea of a longitudinal waveusing the handy model provided by Figure1.6. Use two A5 pieces of paper. Place onesheet so that it covers all except the top fewmillimetres of the diagram. Place the othersheet so that there is a 2 mm slot createdbetween the sheets at the top of thediagram. Now maintaining the 2 mm slotbetween the pages, slide the pages downthe diagram, taking about 4 seconds toreach the bottom of the diagram. As youwatch the slot you should be able to seelongitudinal waves travelling to the right.Try varying your sliding speed. Then figureout how it works!

positionposition

time

time

Figure 1.6 Looking at these wavy linesthrough a slit gives the impression oflongitudinal waves moving to the right.

Modelling a longitudinal wave


Figure 1.7 (a) The ripples on the surfaceof this pond are described as two-dimensionalwaves since energy travels outwards in twodimensions. (b) Energy travelling outward in alldirections, as in this bomb blast, forms athree-dimensional wave.

Seismic wave detectors dont just pick upthe vibrations from earth tremors. Thedemise of the space shuttle Columbia, thesinking of the Russian Kursk submarineand the collapse of the World TradeCenter towers in New York all registeredon different seismographs around theworld.

Physics file familiar example of these (see Figure 1.7a). Earthquakes, amongst othereffects, produce two-dimensional seismic waves that are mechanical wavestravelling across the surface of the Earth. The Sun has a version of these too.Solar flares have been found to be the cause of solar quakes. These two-dimensional waves travel across the surface of the Sun and although theytravel across distances equal to ten Earth diameters, they look just like ripplesin a pond.

When you speak you create three-dimensional waves since the sound waveenergy spreads out in all three dimensions, though obviously the majority ofthe energy travels directly outward from the source. Designers of particularspeaker-systems attempt to ensure that sound waves are spread out equally inall directions. Figure 1.7b shows a three-dimensional pressure wave emittedby a bomb blast.


Scientists use models to link an unknown entity orobservation to something that we are familiar with, inorder to gain a better understanding of it.

Knowledge of general wave properties will allow thepossible wave nature of light to be assessed.

Energy must be present at the source of any wave. All waves involve the transfer of energy without a net

transfer of matter. A substance carrying a wave is called a medium. A mechanical wave is the passing of energy from one

particle to the next within an elastic medium.

A wave pulse occurs when a single disturbance ispassed through a medium.

Continuous waves are created when there is a repet-itive motion or oscillation at the wave source. Energy iscarried away from the source in the form of acontinuous or periodic wave.

Longitudinal waves occur when particles of themedium vibrate in the same direction as the directionof travel of the energy.

Transverse waves are created when the direction of thevibration of the particle of the medium is perpendicularto the direction of travel of the wave energy itself.

1.1 SUMMARY INTRODUCING WAVES

1.1 QUESTIONS

1 Describe two ways in which energy can be transmitted.

2 What is the difference between a continuous wave and apulse?

3 Classify each of the items below as a continuous wave, apulse or neither:

a an opera singer holding a note for a long timeb an explosionc a flag flapping in the windd dominos standing up in a row and the first one is

knocked onto the second, etc.e a tsunami that is caused by a single upward shift in a

section of a seabed.4 One end of a long spring is tied to a hook in a wall and

the spring is pulled tight. The free end is then shaken upand down.

a Is the resultant wave transverse or longitudinal?b Describe the motion of a particle that is part of a

longitudinal wave compared with one that is part of atransverse wave.

5 A slinky spring runs from east to west across the floor ofa room and is held at each end. At one end a persongives one quick shake by moving her hand in a northerlyand then a southerly direction.

a Is the wave in the spring longitudinal or transverse?b Is the wave in the spring continuous or a pulse?c Draw an example of how the spring might look at one

moment in time.6 A slinky spring runs from east to west across the floor of

a room and is held at each end. At one end a personoscillates her hand periodically in an easterly and then awesterly direction.

a Is the wave in the spring longitudinal or transverse?b Is the wave in the spring continuous or a pulse?c Daw an example of how the spring might look at one

moment in time.

7 Which of the following statements is incorrect?

A Mechanical waves are made up of a series of pulses.B Mechanical waves must have a vibrating item at their

sourceC All waves transmit energy but dont transmit

materials.D All waves travel at right angles to the vibration of the

particles in the medium.8 A spring was initially at rest and under slight tension

when a series of compressions were sent along it asshown.

a How many oscillations had the hand completed at themoment shown?

b In what direction are the following points about tomove?i X ii Y iii Z

9 Using apparatus like that shown in Figure 1.3, draw asequence of five or six diagrams showing the passage ofa transverse wave pulse along the entire length of thespring.

10 Explain the following observation: Although transversewaves cannot travel through the middle or lower sectionsof a body of water, they can travel along its surface.

undisturbed spring

Z Y X

Displacementdistance graphsIf a continuous wave was travelling across the surface of water, and we were ableto freeze it instantaneously, a cross-section would look something like Figure1.8a. If the wave then continued, a brief moment later it will have moved slightlyto the right and the water particles will have taken up new positions as shown inFigure 1.8b and then Figure 1.8c. The floating cork, like the particles of themedium itself, demonstrates a vertical vibratory motion. It is displaced up thendown, then up, then down. Instead, a continuous transverse wave could be sentalong a piece of rope or a spring, and the particles of the medium would displaya similar behaviour to the up and down motion of the water particles.


1.2 Representing wave features

(a)

(b)

(c)

wave source

cork now lower

wave travels right originalwaterlevel

crest

trough

Figure 1.8 As the wave moves to the right the displacement of the particles of themedium can be tracked using a cork. (a) The cork is on the crest of a wave. (b) Thecork has moved lower as the wave moves to the right. (c) The cork is now in thetrough of a wave.

A more convenient way of representing waves is to draw a graph of particledisplacement against distance from the source. Keep in mind that the meanposition of each water particle is the undisturbed level (flat surface) of thewater. On the vertical axis we plot the displacement of each particle from itsoriginal level at a particular moment in time. The horizontal axis is used torepresent the various locations across the waters surface. Therefore the graphshows the displacement of all particles along the path of the wave, at aparticular instant. In this case the chosen instant is the wave position shownin Figure 1.8c.

The shape of the graph in Figure 1.9 relates directly to what we see on thesurface of the water. However, these types of graphs can also be used torepresent waves that are not so readily visible. Sound waves in air are often

represented via displacementdistance graphs but in this case the verticalaxis is used to show the forward and backward displacement of the airmolecules as the sound wave passes through. Re-visit Figure 1.5a. If alongitudinal pulse was sent down a spring (by giving a quick push along itsaxis), then the vertical axis could be used to represent the forward andbackward displacement of the particles of the medium.

The speed of wavesRather than just examining one snapshot, a sequence of graphs can be usedto represent a wave that is moving across to the right (see Figure 1.10). Bytracking the progress of one crest as it moves to the right, the speed at whichthe wave is moving can be determined. The use of a dashed line in Figure 1.10is just to help you keep track of the initial trough and crest that were created.Note that points P and Q and all particles of the medium simply oscillatevertically, whilst the crests and troughs move steadily to the right.


Figure 1.10 As each disturbance is createdit will be carried away from the source by themedium.

Part

icle

disp

lace

men

t

Distance from the source

Figure 1.9 The graph of displacementversus distance from the source of a wave iseffectively freezing the wave at a moment intime, in other words taking a snapshot.

Worked example 1.2A.Use the series of graphs shown in Figure 1.10 to determine:

a the average speed of the wave

b the horizontal speed of particle P

c the average vertical speed of particle P between t = 0 s and t = 0.025 s.

Solutiona Since speed is the measurement of the distance an item travels in a

certain time, examining the progress of the first crest it travels fromd = 0.01 m to d = 0.05 m in a time period of 0.100 seconds.

Average speed =

=

=

= 0.40 m s1 or 40 cm s1

b Particle P is vibrating vertically. It has zero horizontal speed.

c Particle P covers a vertical distance of 5 103 m (or 5 mm) in this timeperiod.

Average speed =

=

= 0.20 m s1

In mechanical waves the speed of the wave is largely determined by theproperties of the medium and, of course, by the type of disturbance that isbeing carried by the medium. (Sometimes the speed of a wave can also beaffected by the frequency of the source; this is discussed later.) You may haveobserved a common example of how the properties of a medium can bealtered in order to change the speed of a wave. Try sending a pulse along aslinky spring and make a mental note of how quickly it is carried away. Nowstretch the spring across a greater distance, increasing the tension in thespring, and send a similar pulse along it. You should have been able tonoticeably increase the speed at which the wave travels. Tension is oneexample of a property of an elastic medium that affects wave speed. Table 1.1shows some common waves and typical speeds at which they are carried bytheir medium.

Table 1.1 Typical speeds of waves in some common mediums.

Source of wave Medium Typical speed (m s1)

Mechanical pulse slinky spring 200Guitar plucking guitar string 300Sound source air at 20C 344

water 1450rock 15003500

Infrared waves vacuum (no medium) 3 108

0.0050.025

distance travelledtime taken

0.040.100

(0.05 0.01)0.100



Figure 1.11 Infrared (heat) waves travelaway from the source at the same speed aslight in a vacuum or in air, 3 108 m s1.Different temperatures show up as differentcolours in an infrared photograph.

PRACTICAL ACTIVITY 4The speed of sound by clapand echo

The frequency and period of a waveEvery mechanical wave must have a vibrating source. The rate at which thesource vibrates directly affects the nature of the wave formed. The frequencyof a source is the number of full vibrations or cycles that are completed persecond. For example, a dipping rod in a ripple tank may move up and down30 times each second. It will therefore create 30 crests and 30 troughs on thewaters surface every second. If any given point on the waters surface wereselected, then 30 complete waves would travel past this point per second.Frequency is a measurement of cycles per second (s1), and this unit has beenappropriately named after Heinrich Hertz (18571894) who did importantwork with radio waves. Hence 1 cycle per second (s1) equals 1 hertz (Hz).

The time interval for one vibration or cycle to be completed is called theperiod, T, which is measured in seconds (s). This will also be the time betweensuccessive wave crests arriving at a given point. Since a decrease in thefrequency of a wave will result in a longer period between waves, therelationship between frequency and period is an example of inverse variation.For example, if ten crests pass a given point in 1 second, then the frequency ofthe wave must be 10 Hz and the period of the wave would be one-tenth of asecond or 0.1 s.

Worked example 1.2B.A student lays a long heavy rope in a straight line across a smooth floor.She holds one end of the rope and shakes it sideways, to and fro, with aregular rhythm. This sends a transverse wave along the rope. Anotherstudent standing halfway along the rope notices that two crests andtroughs travel past him each second.

a What is the frequency of the wave in the rope?

b What is the frequency of vibration of the source of the wave?

c How long does it take for the student to produce each complete wavein the rope?

Solutiona Since frequency is defined as the number of complete waves that pass

a given point per second, f = 2 Hz.

b To produce a wave with a frequency of 2 Hz, the source must have thesame frequency of vibration; that is, 2 Hz.

c f =

T = = = 0.5 s

It takes 0.5 s for each cycle to be completed.

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1T

1T


The FREQUENCY of a wave source, f, in hertz (Hz), is the number of vibrationsor cycles that are completed per second.

Or the frequency of a wave travelling in a medium is the number of completewaves that pass a given point per second.

FREQUENCY, f =

where f = frequency of the wave in hertz (Hz)T = period of the wave in seconds (s)

1T

These ideas about waves can be investigated in theInteractive Tutorial entitledThe Wave Equations.

Displacementtime graphsThe effects of mechanical waves can be investigated using displacementtimegraphs. In these graphs the movement of one particle of the medium ismonitored as a continuous wave passes through. As with the previous graphswe studied, the vertical axis may be used to represent displacementsperpendicular to the waves direction (as in transverse waves) or parallel to thewaves direction (as in longitudinal waves). Regardless, the displacement ismeasured relative to the mean position of the particle. Since the horizontal axisindicates time values, the period of the continuous wave can be directly readfrom the graph. Figure 1.12 shows the displacementtime graph that wouldapply to the situation described in Worked example 1.2B. Note that the graphcovers two complete cycles; that is, two complete waves have passed by.

Wavelength and amplitudeRecall that earlier we examined graphs that show the displacement of allparticles along the path of a continuous wave, at a particular instant. Graphsof particle displacement versus distance from the source can be used todetermine the wavelength of a continuous wave. Examine Figure 1.13. Clearlythere are particles within the medium that have identical displacements at thesame time, such as points A and B. The wavelength of a continuous wave is thedistance between successive points with the same displacement and movingin the same direction. These points are said to be in phase with one another.The symbol used for wavelength is the Greek letter lamda, . Like all lengthmeasurements in physics, the standard unit used is the metre (m).

In Figure 1.13 the points X and Y have the same displacement and directionof movement and so they can also be described as being one wavelength apartfrom each other. Note that although points P and Q have the same dis-placement, they will not be moving in the same direction. They are only apart from one another. In the next section we will examine how the frequencyof the wave source, and the velocity that the medium allows the wave,combine to determine the wavelength of the wave that is produced.

The amplitude, A, of a wave is the value of the maximum displacement ofa particle from its mean position. The displacement of particles in acontinuous wave will vary between a value of A and A, as shown in Figure 1.13.The more energy provided by the source of the wave, the larger the amplitudeof the wave. For example, in water waves the amplitude obviously correspondsdirectly to the height of the wave. In sound waves the amplitude determinesthe loudness of the sound.

12


Figure 1.12 When determining the period of a wave directly from a displacementtime graph it does not matter at which part of the cycle you begin the periodmeasurement.

Keep in mind that displacementtimegraphs are looking at the motion of aparticular particle. Recall our originaldefinition of a wave as involving energymoving in a medium and realise thatthese graphs are not showing energytravelling. Therefore these diagrams arenot actually graphing a wave. The familiarshape of this graph occurs because themotion of the particle is periodic; that is,a repeating cycle.

Physics file

In many of the waves examined in thischapter there is no decrease in amplitudeshown as the wave travels through itsmedium. This is an idealisation. You willhave noticed that pulses sent alongsprings will die out eventually. Internalresistance within real springs turns someof the waves energy to heat. The energyof a circular wave is spread over a largerand larger wavefront as the circumferenceof the circular wavefront grows. As itmoves outward, each section decreasesin amplitude because it carries a smallerportion of the waves total energy.

Physics file

PRACTICAL ACTIVITY 5Waves in a ripple tank


Figure 1.13 When determining the wavelength of a wave directly from adisplacementdistance graph it does not matter at which part of the cycle you beginthe wavelength measurement.

All sorts of waves, such as the circular water waves seen inFigure 1.14a, can also be represented in diagrams like thatshown in Figure 1.14b. Lines are used to represent a certainpart of the wave, such as the crests. If the diagram weredrawn to scale the distance between the lines wouldrepresent the wavelength, . These diagrams areparticularly useful should you want to indicate the regionover which the wave energy has spread.

In 1678 Christiaan Huygens suggested a model thatprovides an explanation for how waves are carried througha medium. His model coincides with what we see insituations like that shown in Figure 1.14a. Huygenssprinciple is a method that uses geometry to predict the new position of a wavefront, if the original position of the

Huygenss principle

PHYSICS IN ACTION

Figure 1.14 (a) Circular water waves. (b) Evenly spaced lines can represent the crests of a wave travelling outward, according toHuygenss principle.(c) Every point on a wavefront is a source of secondary circular wavelets, according to the principle.

(a)

(b) (c)


A mechanical wave can be represented at a particularinstant by a graph of particle displacement againstdistance from the source.

The frequency of a wave, f, is the number of vibrationsor cycles that are completed per second, or the numberof complete waves that pass a given point per second.Frequency is measured in hertz (Hz).

The period, T, is the time interval for one vibration orcycle to be completed.

Frequency, f = where f is the frequency of the wave

in hertz (Hz), and T is the period of the wave inseconds (s).

A graph of particle displacement versus time can bedrawn for the particles of a medium that is carrying acontinuous wave. The period of the wave can bedirectly read from this graph.

Graphs of particle displacement versus distance fromthe source can be used to determine the wavelengthof a continuous wave.

The wavelength, , of a continuous wave is the distancebetween successive points having the same displace-ment and moving in the same direction; that is, thedistance between points that are in phase.

The amplitude, A, of a wave is the value of themaximum displacement of a particle from its meanposition.

1T

1.2 SUMMARY REPRESENTING WAVE FEATURES

wavefront is known. The principle states that every pointon a wavefront may be considered the source of smallsecondary circular wavelets. These wavelets spread outwith exactly the same speed as the original wavefront. Thenew wavefront is then found by drawing a tangent to all ofthe secondary wavelets. This is called the envelope of thewavelets and is shown in Figure 1.14c.

Figure 1.14c shows the points on a wavefront that are

sources of secondary circular wavelets. These waveletsmove at speed v and so during time interval t cover adistance of vt. The speed, v, has been assumed to be thesame for all wavelets. Although we have only examined thespread of a circular wave, Huygens was renowned for theuse of his principle in explaining the reflection andrefraction of waves at boundaries (which is discussed laterin this text).

1.2 QUESTIONS

1 Calculate the frequency and period of:

a a spring that undergoes 40 vibrations in 50 seconds

b a pendulum that completes 250 full swings in oneand a half minutes.

2 In a ripple tank the trough of a water wave travels 70 cmin 2.5 seconds. Calculate the speed of the wave inmetres per second.

3 What usually happens to the amplitude of the vibration ofa circular water wave as it spreads out? Why?

4 A pebble is dropped into a pool and after 3.00 seconds24 wave crests have been created and travelled out fromwhere the pebble entered the water. What is thefrequency and period of the water wave that wascreated?

5 A piston in a car engine completes 250 complete up-and-down movements every half a minute.

a What is the frequency of vibration of the piston?

b What is its period?

c Assuming that the piston started from a centralposition and moved up. Where will it be after:

i 1 period? ii 1 periods? iii 1 periods?

6 Which of the following statements is correct?

A Period is the measurement of the length of a wave.

B The amplitude of a wave is dependent upon thefrequency.

C The more energy put into a wave the greater thewavelength.

D The more energy put into a wave the greater theamplitude.

7 Examine the wave represented in Figure 1.10. What isthe wavelength of the wave?

12

14

8 A longitudinal wave enters a medium and causes itsparticles to vibrate periodically. Draw adisplacementtime graph that could demonstrate themotion of the first affected particle of the medium for thefirst two cycles. Begin with a positive displacement; i.e. inthe direction of travel of the wave.

9 The displacementdistance graph shows a snapshot of atransverse wave as it travels along a spring towards theright.

a Use the graph to determine the wavelength and theamplitude of this wave.

b At the moment shown, state the direction in whichthe following particles are moving: Q, S.

c Assuming that the wave is travelling at 12 m s1 tothe right, and no energy is lost, draw thedisplacementdistance graph for this wave 0.05seconds after the moment shown. Label the points P,Q, R and S.

10 The displacementtime graph shows the motion of asingle air molecule, P, as a sound wave passes bytravelling to the right.

a Use the graph to determine the amplitude, periodand frequency of this sound wave.

b State the displacement of the particle P at: i t = 1 ms ii t = 2.5 ms iii t = 5.5 ms

c Draw the displacementtime graph for the particle,Q, which is positioned half a wavelength to the rightof particle P. Show the same 4 ms time interval.

d If sound is actually a longitudinal wave, why does thisgraph look more like a transverse wave?


The wave equationThe frequency of a source of a mechanical wave and the velocity of that wavein the medium together determine the resulting wavelength of the wave.For example, a horizontal bar vibrating at frequency, f, may be used as thedipping element in a laboratory ripple-tank as shown in Figure 1.15. Onceone crest is created, assume that it travels away from the source at a knownspeed, v.

Since the definition of speed is:

speed =

This can be rearranged to:

distance travelled = speed time taken.

Consider the first period, T, of the waves existence. The distance that thefirst wave will be able to cover before the next wave is created behind it isdetermined by the speed at which the medium allows the wave to travel. Thedistance that the first wave travels during one periodby definitionis thewavelength of the wave, . Therefore we acknowledge that the distancetravelled = when the time taken = T.

Substituting into:

distance travelled = speed time taken

= v TThe frequency and period of a wave are inversely related:

T =

Hence, the above relationship can also be expressed as:

=

Note that for a medium of a given speed, the use of a higher frequencysource would result in waves that are closer together; that is, waves of a shorterwavelength. A low frequency source would produce longer wavelength waves(see Figure 1.16). For a given wave speed:

1f

vf

1f



1.3 Waves and wave interactions

Figure 1.15 The medium carrying the waveand the frequency of its source togetherdetermine the wavelength of a wave.

The WAVE EQUATION links the speed, frequency and wavelength of a wave:

v = fwhere v = speed of the wave in metres per second (m s1)

f = frequency of the wave in hertz (Hz), and

= wavelength of the wave in metres (m).

An implication of the wave equation that is worth noting is that a sourcethat has a specific frequency of vibration is able to produce waves of differentwavelengths, depending upon the medium that carries the wave. Consider asubmarine that puts out a high frequency tone of 20 000 Hz. If this samefrequency tone were sent both into the water and into the air, the wavesproduced in the water would have a much longer wavelength that the wavesproduced in the air. This is because sound waves travel about four times fasterin water than in air (see Figure 1.17). For a source of a given frequency:

v

Worked example 1.3A.A person standing on a pier notices that every 4.0 seconds the crest of awave travels past a certain pole that sticks out of the water. The crestsare 12 metres apart from one another. Calculate:

a the frequency of the waves

b the speed of the waves.

Solutiona The period of the wave is 4.0 s.

Since f =

f =

= 0.25 Hz

b Since the crests are 12 m apart the wavelength is 12 m.

v = f= 0.25 12

= 3.0 m s1

Waves meeting barriersMechanical waves travel through a medium. Commonly a situation will occurin which the wave travels right through to a point where the mediumphysically ends. An example of this is the wave created as a child leaps into apool; it travels until it reaches the pool wall. At the boundary of the mediumthe energy that was being carried by the wave may undergo differentprocesses. Some of the energy may be absorbed by or transmitted into a newmedium, and some energy may be reflected.

1

4.0

1T


Figure 1.16 (a) For a medium of a given speed, the use of a low frequency sourceproduces waves with a long wavelength. (b) With less time between the creation ofsuccessive waves, a high frequency source produces waves with a shorterwavelength.

Figure 1.17 Since sound waves travel muchfaster in water than in air, the waves producedby a tone of a given frequency have a muchlonger wavelength when they travel throughwater than when they travel through air.

See the Medical Physics DetailedStudy for a study of ultrasoundwaves in the body.

PRACTICAL ACTIVITY 6Reflection of waves in a rippletank


The extent to which these processes occur depends on the properties of theboundary. We shall examine the case of a transverse wave pulse travelling in aheavy rope that has one end tied to a wall. As shown in Figure 1.18a the wavetravels to the boundary and we can see that it is reflected with almost no energyloss since the original amplitude is maintained. The wave, however, has beeninverted; this can also be described as a reversal in phase. (The definition ofphase was discussed in the previous section.) Since a crest would reflect as atrough and a trough would reflect as a crest, we can say that the phase of thewave has been shifted by .

Now consider the situation where the end of the rope is instead free tomove. As shown in Figure 1.18b, the wave travels to the end of the rope and wecan see that it is reflected with no reversal in phase. Since a crest would reflectas a crest and a trough would reflect as a trough, we can say that there was nochange of phase.

12

A WAVE REFLECTING FROM THE FIXED END of a string will undergo a

phase reversal; that is, a phase shift of .2

A WAVE REFLECTING FROM THE FREE END of a string will not undergo aphase reversal.

The phase change of a wave on reflectionfrom a fixed end can be explained interms of Newtons third law of motion.When the pulse arrives at the fixture therope exerts a force on the fixture. Thefixture exerts an equal and opposite forceon the rope. This produces a pulse that isin the opposite direction to the originalpulse; that is, a change in phase hasoccurred.

Physics file

Figure 1.18 (a) The reflection of a wave at an unyielding boundary produces a phaseshift of . Note that otherwise the shape of the wave is unaltered. (b) The reflectionof a wave at a free-end boundary does not produce a phase shift.

12

The stealth bomber is an aircraft that is designed so that itsbody is as poor a reflector as possible. The main way inwhich a passing aircraft is detected by others is with the useof radar. A radar transmitter sends out pulses of radiowaves or microwaves and a receiver checks for anyreflections from passing aircraft. By analysing thereflections, radar systems can work out the position, speedand perhaps even the identity of the passing aircraft.

Stealth aircraft are supposed to create as little reflectionof these waves as possible. The shape of the stealth aircraftis the most important factor. It does not have any largevertical panels on the fuselage that would act like mirrors,nor a large vertical tail. It has no externally mounteddevices such as missiles or bombs. It does not include anysurfaces that meet at right angles. These would act like thecorners in a billiard table and bounce the waves right backto their source. Instead curved surfaces on the stealthbomber are designed to reflect waves sideways or upwardwherever possible. A thick coat of special paint that

absorbs radio waves is used on its surface. Although notcompletely undetectable, with the right shape and coatinga large stealth plane can produce the same amount ofwave reflection as an average sized marble!

Reflections NOT wanted!

PHYSICS IN ACTION

Figure 1.19 The reflection of radar waves from aircraftusually reveals their position but the stealth plane is designedfor minimal reflection.

Superposition: waves interfering with wavesIn the case of a continuous wave being sent toward a boundary, a situation canbe created where two waves may be travelling in the one medium, but indifferent directions. The incident waves will meet the waves that have alreadyreflected from the boundary. When two waves meet they interact according tothe principle of superposition.

Consider a spring where a transverse pulse has been sent from each end, asshown by the sequence of events in Figure 1.20. When the pulses reach thesame point in the spring the resulting wave will be the sum of the displacementproduced by the individual pulses. The principle of superposition is thereforethe same as the addition of ordinates process that is carried out on graphs.Simply sum the y-values of each of the pulses to see the resulting wave.

In Figure 1.20 the initial pulses have particle displacements in the samedirection and therefore constructive interference occurs. Notice that afterinteracting with each other, the two pulses have continued on unaffected. Thisis an observed property of waves. They are able to pass through one another,momentarily interact according to the superposition principle, and thencontinue on as if nothing had happened.


The principle of SUPERPOSITION states that when two or more waves travel ina medium the resulting wave, at any moment and at any point, is the sum of thedisplacements associated with the individual waves.

When a note is played on a musicalinstrument sound waves with manydifferent wavelengths are producedsimultaneously. The richness of a tone islargely determined by how many differentwavelengths make up the sound wave.The tone with the longest wavelengthdetermines the overall perceived pitch ofthe note but the number of overtones(other wavelengths present) will add to itstimbre.

Physics file

Figure 1.20 Superposition of two pulses of the same amplitude travelling toward oneanother.

PRACTICAL ACTIVITY 7Diffraction of continuouswater waves

PRACTICAL ACTIVITY 8Interference of water waves

In Figure 1.21 destructive interference occurs since the initial pulses haveparticle displacements in opposite directions. If the crest of one pulse hasexactly the same dimensions as the trough in the approaching pulse then thetwo pulses will momentarily completely cancel each other out, as shown inFigure 1.21. If the amplitude of one of the waves is larger than the other thenonly partial cancellation will occur.

In the case of interference between continuous waves, the principle ofsuperposition is still applicable. If two waves are exactly in phase and aretravelling in the same direction, then constructive interference will occuralong the entire length of the wave. The two waves need not have the sameamplitude. In Figure 1.22 one wave is twice the amplitude of the other waveand the resultant wave is shown.

Interesting effects are observed when two waves of different wavelengthsare travelling in the same direction and interfere with one another. Figure 1.23shows the addition of two waves, where one wavelength is exactly three timeslonger than the other. This is a relatively simple example. Imagine thecomplexity of the sound-wave patterns produced when instruments in anorchestra are played simultaneously. Or of the wave patterns that areproduced on the surface of water in a busy harbour.


Figure 1.21 Superposition of two pulses of equal but opposite amplitudes travellingtoward one another.

Figure 1.23 The addition of waves of different wavelengths results in complex wavepatterns.

Figure 1.22 The superposition of continuouswaves that are in phase and travelling in thesame direction will result in constructiveinterference.

We have looked at how waves can reflectback along a string from a fixed end.Essentially this is what happens to thewaves sent along a bowed violin string ora plucked guitar string. The numerousreflected waves add together accordingto the principle of superposition withsome important effects. For each modeof vibration shown in Figure 1.24, atsome spots on the string constructiveinterference will occur. In other spotsdestructive interference occurs. Sinceeach particular mode of vibration has setlocations for these spots, the wave iscalled a standing wave.

Physics file

Figure 1.24 One mode in which a stringcan vibrate involves destructiveinterference happening right at thecentre point of the string.


We have seen how a wave can spread out from a pointsource, but waves are also capable of bending aroundobstacles or spreading out after they pass through a narrowgap. This bending of the direction of travel of a wave iscalled diffraction. Figure 1.25 shows the diffraction ofwater waves as they pass by an obstacle.

Diffraction effects can be seen with two-dimensionalwaves, such as on the surface of water, and also with three-dimensional sound waves. This explains why we can hearsounds that were originally made around the corner of abuilding. The sound waves bend their direction of travelthat is, diffractaround the corner of the building to reachthe listeners ears.

The extent to which diffraction occurs depends on therelative dimensions of the aperture or obstacle that thewave passes, and the wavelength of the wave. Mostnoticeable diffraction occurs if the wavelength is at least aslarge as the aperture is wide. When waves of the samewavelength are sent through large and narrow apertures asin Figure 1.26, only waves passing through the narrowaperture produce noticeable diffraction.

Spreading water waves produce interference patternsthat are characteristic of waves. Consider two sources ofspherical waves (Figure 1.27). In some locations construc-tive interference occurs and waves of relatively largeamplitude are seen. These regions have lots of contrast inthe photograph; that is, alternating bright and dark bandsare seen. In other regions destructive interference occurs.Troughs arriving from the other source always cancel out

the crests that arrive at these locations, and the surface ofthe water remains relatively undisturbed. The regions ofdestructive interference appear grey and flat in thephotograph. These regions of destructive interferenceappear to radiate from a point between the sources.

Both diffraction and interference effects are onlyobserved when energy is being carried by waves, not whenenergy is being carried by particles.

Diffraction and interference effects

PHYSICS IN ACTION

Figure 1.25 Rather than only travelling directly forward, noticehow the wavefronts spread out to fill the region behind the obstacle.

Figure 1.26 Significant diffraction occurs when the wavelengthis at least as large as the aperture.

Figure 1.27The interference pattern produced by two point sources in phase.

Now we can look at light!Now that we have put together the rules describing the characteristics ofwaves, the question as to whether light has a wave nature can be addressed.Waves have numerous characteristics and they have been worth examining intheir own right. We have been able to conclude that: waves involve the transfer of energy without an overall transfer of matter mechanical waves require a vibrating item at their source and a medium to

carry them waves can be categorised as longitudinal or transverse the wave equation, v = f , describes the relationship between the speed,

frequency and wavelength of a wave waves can reflect at boundaries and this will sometimes produce a change

of phase waves can be added according to the principle of superposition and this can

result in constructive or destructive interference.

In Chapter 2 we will go on to discuss whether it is appropriate to use wavesas our chosen model for light. For this to be fitting, light must appear to behavelargely in the same manner as waves do. That is, if a wave model for light is tobe accepted, then it will need to explain the known behaviours of light. A verysuccessful model would illustrate all of the behaviours of light. This is notlikely. It is more likely that we will be able to make use of the insight that wavesprovide, and use this insight to further our understanding of the nature of light.


The frequency of the source and the speed of thewave in the medium determine the wavelength of amechanical wave.

The wave equation states: v = f , where v = speed of thewave in metres per second (m s1), f = frequency ofthe wave in hertz (Hz), and = wavelength of the wavein metres (m).

For a wave of a given speed: .

For a source of a given frequency: v. A wave reflecting from a fixed end of a string will under-

go a phase reversal; that is, a phase shift of .

A wave reflecting from a free end of a string will notundergo a phase reversal.

The principle of superposition states that when twoor more waves travel in a medium the resulting wave,at any moment, is the sum of the displacementsassociated with the individual waves.

Constructive interference occurs when two wavesmeet that have particle displacements in the samedirection.

Destructive interference occurs when two waves meetthat have particle displacements in oppositedirections.

2

1f

1.3 SUMMARY WAVES AND WAVE INTERACTIONS

1.3 QUESTIONS

1 a What happens to the wavelengths of the waves in aripple tank if the frequency of the wave source isdoubled?

b What happens to the speed of the waves in a rippletank if the frequency of the wave source is halved?

2 The source of waves in a ripple tank vibrates at afrequency of 15.0 Hz. If the wave crests are 40.0 mmapart, what is the speed of the waves in the tank?

3 A wave travels a distance of 50 times its wavelength in10 seconds. What is its frequency?

4 A submarines sonar equipment sends out a signal with afrequency of 35 kHz. If the wave travels at 1400 m s1,what is the wavelength of the wave produced?

5 Which of the following statements is incorrect?

A When two pulses interact the resulting wave, at anymoment, is the sum of the displacements associatedwith the individual waves.

B After two waves interact with each other they willcontinue on through the medium unaffected.


C For two pulses to interfere destructively they musthave opposite amplitudes.

D For two continuous waves to interfere constructivelythey must have identical amplitudes.

6 Will a transverse wave reaching the fixed end of a stringundergo a phase reversal?

7 Two waves are travelling in the same direction in amedium. They undergo constructive interference alongthe entire length of the wave. What two statements canbe made about the two waves?

8 Assuming the following diagram shows the displacementdistance graphs of two waves at a particular instant,show the addition of the two waves according to theprinciple of superposition.

9 Draw the resultant displacement versus distance graphfor two superimposed continuous waves that are inphase and travelling in the same direction. Each wavehas a wavelength of 4 cm and amplitude of 1 cm. Showtwo complete cycles.

10 Draw the resultant displacement versus distance graphfor two superimposed continuous waves travelling in thesame direction. Each wave has a wavelength of 4 cm andamplitude of 1 cm, but one wave is one-quarter of awavelength behind the other.

The following information applies toquestions 1 to 3. A pulse is travellingalong a light spring. The diagram belowshows the position of the pulse at

t = 0 s. The pulse is moving at a speedof 40 cm s1 to the right.

1 Use a set of scaled axes to drawthe displacementdistance graphfor the pulse at the momentshown.

2 Draw the displacementdistancegraph for the pulse 0.5 secondslater. Clearly show the location ofpoint P.

3 Draw the displacementtimegraph for the point Q for a time

interval of 2.0 seconds, beginningat t = 0.

4 List an example of a one-, two- andthree-dimensional wave.

5 A guitar string is plucked near oneend. A wave moves along thestring and another wave isproduced in the air. State whethereach wave is transverse orlongitudinal.

The following information applies toquestions 6 to 9. The diagram showstwo successive amplitudedistancegraphs for a periodic transverse wavetravelling in a string. The time intervalthat passed between the tracings of thetwo graphs is 0.20 s. The graphs aredrawn exactly to scale.

6 State the amplitude of the wave.

7 State the wavelength of the wave.

8 Calculate the velocity of the wave.

9 Calculate the frequency and periodof the wave.

10 Which of the followingstatement(s) is/are incorrect (oneor more answers)?

A All mechanical waves require amedium to carry the wave.

B All mechanical waves transferenergy.

C In wave motion some of thematerial is carried along withthe wave.

D Mechanical wavespermanently affect thetransmitting medium.

CHAPTER REVIEW


11 What is the period of the wavethat:

a involves 5.0 crests of waterlapping against a breakwatereach 20 seconds?

b is produced by a flute playingthe note middle C (512 Hz)?

12 Find the frequency of the wavesthat have periods of:

a 0.35 s

b 4.0 103 s

c 102 s.

13 A wave pulse is sentsimultaneously from both ends ofa spring. When the pulses meetthey momentarily completelycancel out one another.

a What is the term thatdescribes this occurrence?

b Make statements about threefeatures of the wave pulses.

14 A transverse wave travels along astring towards an end that is freeto move. Which of the followingstatements is true?

A The wave will reflect with nophase change.

B The wave will reflect with a

phase change of .

C The wave will not be reflected.

D The wave will reflect fasterthan the incident wave.

15 Waves travelling in a ripple tankhave a wavelength of 7.0 mm andtravel at 60 cm s1. What is thefrequency and period of thewaves?

16 One end of a long spring is firmlyconnected to a wall fitting. Brieflyexplain how a transverse wave canbe created and carried by thespring.

The following information applies toquestions 17 to 20. Wave A has awavelength of 4.0 cm, a period of 2.0seconds and an amplitude of 1.5 cm.Wave B has a wavelength of 2.0 cm, aperiod of 1.0 second and an amplitudeof 1.5 cm.

17 Draw a scaled displacementdistance graph for wave A. Showtwo full waves.

18 Draw a scaled displacementdistance graph for wave B. Showfour full waves.

19 If wave A and wave B were sentinto the same medium and theyare travelling in the samedirection, draw the resultantdisplacementdistance graph.Show two full waves.

20 Draw a displacementtime graphfor a particle in the medium thatcarries wave A only. Show twocomplete cycles.

2

CHAPTER REVIEW

It is a common trait of humans that when we seek to understandsomething we will intuitively attempt to link the unknown withthe known. In your earlier schooling a physical representationor model was probably used to teach you about natures watercycle, or multiplication, or the properties of gases. Young studentsbenefit from the use of tangible items such as models; things thatcan be seen and touched. As we grow, our knowledge andunderstanding can still benefit from the use of a modellingapproach, but our models can be more sophisticated. Whencomputer-generated pictures were used to model the complexequations of fractal geometry they had an amazing similarity tosome structures found in nature. Fractal images model thingssuch as coastlines and snowflakes and they have become popularworks of art.

A model is a system of some type that is well understood andthat is used to build a mental picture or analogy for an observedphenomenon, in our case the behaviour of light. A good model willappear to behave in the same manner as the entity beinginvestigated. A model for light needs to be able to explain theobservations of light that have already been made and ideally itwould predict new behaviours. Therefore, throughout thischapter, when deciding upon a model for light we must examineeach of its known behaviours in turn and assess the effectivenessof the chosen model.

you will have covered material

from the study of the wave-like

properties of light including:

wave and ray models for light

modelling reflection and

refraction

refractive index and Snells law

total internal reflection

optical fibres, and material

and modal dispersion

electromagnetic radiation

colour components of white

light and dispersion

polarisation of light waves.

CHAPTER 2

BY THE END OF THIS CHAPTER

Two models for light


Now that we have a thorough appreciation of the properties of waves, thequestion can be asked: Is light a wave? If a wave is defined as the sum of itsproperties, does light exhibit all of the properties that are known to belong towaves?

Curiosity about the nature of light has occupied the minds of physicists forcenturies. The beginning of human interest in the nature of light dates back tothe ancient Greek, Arabian and Chinese philosophers. In the early 19thcentury, evidence suggested that light could be modelled as a wave since itexhibited the same set of properties as other things that had already beendefined as waves: water waves, sound waves, vibrations in springs and strings.If light exhibits sufficient properties in common with these known waves, thensurely it too could be assumed to be a wave?

The story of the development of a scientific model for light is notstraightforward. The discussion of light as a wave did not exist in isolation. Thegiants of physics became embroiled in a famous ongoing scientific debate thatposed the question: Is light made up of particles or waves? In this section welook at how the very simplest behaviours of light can be readily modelled aseither particles or waves.

Modelling straight-line propagationLight streaming through trees on a misty morning, the projectors beam in adusty cinema, our limited view when peeping through a keyhole and thedistinct shape of shadows are all evidence for the straight-line or rectilinearpath of light. These examples provide evidence that lighttransmitted in auniform medium (i.e. a substance which is unchanging in its constitution)travels in straight lines. Our awareness of the rectilinear propagation of lightallows us to judge the distance to objects. The mechanism by which our eyesand brain interpret a three-dimensional world is complex, but it relies on theassumption that light in a uniform medium travels in straight lines.

The following simple experiment can be performed to demonstrate thatlight travels a straight path in a uniform medium. Make a pinhole in each ofthree identical pieces of card. Place card A close to a light source, and positioncard B a little further away, as shown in Figure 2.1. Then, holding card C in frontof your eye so that you can always see through the hole, adjust its position sothat you can see the light from the lamp. This will only be possible when allthree pinholes lie in the same line; that is, when the pinholes are co-linear. Theconclusion that can be drawn is that light must travel in straight lines.

This property of light was first modelled by considering that light wasparticle-like in nature. Consider a beam of light shining from a powerful torch.If light is assumed to be corpuscular or particle-like in nature then thedirection of travel of the light energy can be represented by rays (Figure 2.2a).The idea of a light ray is a useful concept as it can successfully model thebehaviour of light in the situations illustrated. A beam of light can be thoughtof as a bundle of rays. A strong light source, such as the Sun, could thereforebe thought of as producing a very large number of light particles or rays.

Light sources, in conjunction with other optical elements, such as lenses ormirrors, can produce rays of light that diverge, converge or travel parallel toeach other (Figure 2.2b). In each case the rays are an indication of the direction

2.1 Modelling simple light properties

Figure 2.2 (a) A beam of light is made up ofa bundle of rays. (b) Rays can be diverging,converging or parallel to one another. (c) Anidealised point source of light emits rays oflight in all directions. (d) Very distant sourcesof light are considered to be sources ofparallel rays.

Figure 2.1 Light from the lamp can only beseen if the pinholes lie in a straight line. Thismeans that light must travel from the lamp tothe eye along a straight line.

BA C

divergingrays

convergingrays

parallelrays

(a)

(b)

(c)

(d)

of travel of the light, essentially light is being modelled as a stream of particles.The incandescent (filament) light globes and fluorescent tubes in your homeemit light in all directions. A point source of light is an idealised light sourcethat emits light equally in all directions from a single point (Figure 2.2c). Nosingle point source of light exists in reality, but a small filament lamp can beconsidered a good approximation.

Lasers and special arrangements of light sources with mirrors or lenses canproduce parallel rays of light in a beam. Very distant point sources of light canalso be considered to be sources of parallel light rays. For example, on theEarth we treat the light rays that reach us from the Sun as though they wereparallel to each other. This is because at such a large distance from the source,the angle between adjacent rays would be so tiny as to be considered negligible(Figure 2.2d). Later in this study we will also see how the ray model of lightconveniently allows us to represent and understand the behaviour of light asit interacts with mirrors and lenses to form images.

Although a particle description for light and the accompanying ray modelare convenient for representing the behaviour of light in all of these cases, ithas long been understood that light is not made up of ordinary particles. Lightinvolves the transfer of energy from a source, but there are no tangibleparticles carrying this energy. With developing technology over the last twocenturies physicists have been able to make more and more sophisticatedobservations of light. Later in the chapter we will see that a more refined modelof light incorporates the wave-like properties of light. The ray approach is stilluseful. If light is considered to be a wave emanating from its source, then raysmay simply be used to represent the direction of travel of the wavefronts (seeFigure 2.3). The point source of light discussed above may be considered to bea point source of spherical wavefronts, like the ripples that travel out from astone dropped into a pond (Figure 2.4).

Modelling reflectionThe reflection of waves was discussed in Chapter 1. Light has been observedto obey the same laws of reflection that apply to waves and so evidence isprovided for the argument that light is a wave. Using a wave model, thereflection of light would be represented as a series of wavefronts striking asurface and reflecting as shown in Figure 2.5. However it is far more commonto model the reflection of light using ray diagrams and the conventionsassociated with them.

Consider the plane mirror drawn in Figure 2.6. We define a normal to thesurface of the mirror as the line perpendicular (at 90) to the mirrors surface

Two models for light 29

rays traveloutwardfromtorch

wavefrontstravel outward fromtorch

Figure 2.3 Rays can be used to representthe direction of travel of light waves leaving thetorch.

point source

sphericalwavefrontstravel outwards

Figure 2.4 A point source of light may beconsidered to be a point source of sphericalwaves. Both the particle and the wave modelare consistent with the observation that theintensity reduces with the square of thedistance from the source.

PRACTICAL ACTIVITY 9Reflection in a plane mirror

Figure 2.5 When studying reflection, ray diagrams are the most convenient way ofrepresenting the path of light.

(a) (b) (c)

at the point where an incoming or incident ray strikes the mirror surface.The angle made between an incident ray and the normal is the angle ofincidence, denoted i. The ray strikes the mirror and reflects with an angle ofreflection, r, which is the angle between the reflected ray and the normal.

Experiment shows that whenever reflection occurs, the angle of incidencealways equals the angle of reflection. In addition, the light reflects in such away that the incident ray, the normal and the reflected ray all lie in the sameplane. The law of reflection can then be re-stated using a ray model for light.

A normal household mirror is constructed with three separate layers: a layerof transparent glass, a thin coating of aluminium or silver deposited onto theglass to reflect the light and a backing layer of protective paint (Figure 2.7). Whena beam of light strikes the surface of the mirror a tiny amount of the light energy(about 4%) is reflected from the front surface of the glass, but most of the lightcontinues to travel through the glass and is reflected from the metal surface atthe back. These reflected rays produce the image that is seen in the mirror.

Regular and diffuse reflectionTo some extent at least, light will reflect from all surfaces, but only somesurfaces will produce a clearly defined image. If parallel rays of light are inci-dent on a plane mirror or a flat polished metal surface, they will remain parallelto each other on reflection (Figure 2.8a). This is regular reflection (sometimescalled specular reflection) and, as a result, a clear image can be produced.Common examples of regular reflection include the reflection of light fromplane mirrors, glossy painted surfaces and still water such as in a lake.

When light is reflected from a roughened or uneven surface, it is scatteredin all directions as shown in Figure 2.8b. This is diffuse reflection. Parallel raysof incident light will be reflected in what seem to be unpredictable directions.Each ray obeys the law of reflection, but the surface is irregular so that normalsdrawn at adjacent points have completely different directions. Thus, light isreflected in many different directions. Most materials produce diffusereflection. For example, when looking at this page, you can see the printingbecause the lighting in the room is reflected in all directions due to diffusereflection. If the page behaved as a regular reflector, you would also see the(reflected) images of other objects in the room.

Diffuse and regular reflection are the two extreme cases of how light can bereflected. In reality most surfaces display an intermediate behaviour. Forexample, the pages of a glossy magazine may allow a blurry image of thereaders face to be formed, but the printing can still be seen. The surfaceproduces reflection that lies somewhere between pure diffuse reflection andpure regular reflection. Can you think of any other surfaces that do this? Whatdo they all have in common?

To predict the extent to which diffuse and regular reflection occurs at asurface, one must examine the surface on a microscopic scale. If theirregularities in the surface are small compared with the wavelength of theincident light, then regular reflection occurs. If the irregularities arecomparable in size to the wavelength of light, then more diffuse reflectionoccurs. The wavelength of light is discussed more fully later in the chapter.


Figure 2.7 Most of the incident light on amirror is reflected from the silvered surface atthe back of the mirror. The glass on the frontand the paint on the back serve to protect thereflective surface from damage.

incident ray

glass layermetal layerpaint layer

~4%

~96%

Figure 2.6 When light reflects from a plane mirror, the angle of incidence e

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