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transverse±¬±w±«Õ#XB%±vðReview of the Nature of Waves±ýðReview of the Nature of Waves±þðDefinition of Propagation±ÿÒŽ$U:EX:*.zpew.Ò(‘$U:REV:*.zpew.Ò<”$U:DEF:*.zpew.ÒP—$U:DEF:*.zsiw.Òd—$U:REV:*.zsiw.Òxš$U:DEF:*.zwvl.Ò‹$U:EX:*.zwvl.ÒŸ $U:REV:*.zwvl.Ò³£$U:DEF:*.zwvf.ÒƦ$U:EX:*.zwvf.ÒÚ©$U:REV:*.zwvf.Òî¬$U:DEF:*.zamp.Ò¯$U:EX:*.zamp.Ò²$U:REV:*.zamp.Ò)µ$U:DEF:*.zper.Ò=µ$U:REV:*.zper.ÒQ¸$U:DEF:*.zher.Òe¸$U:REV:*.zher.Òy»$U:DEF:*.zvel.Ò¾$U:REV:*.zvel.±‡±z±‰±Š±‹±…±{±Ž±±|±—±˜±~±ž±±’±}±‰±Š±‹±Œ±±Ž±±±’±—±˜±ž±‹±Œ±±‘±’±Ž±±±‘±’±‘±’±—±˜±“Ò#XC%>Õ#XC%±Ÿ³‚ðPeriodic Waves±ƒ±„±‰±Š±‹±Œ±±Ž±±±‘±’±“ÒGN#XC%>Õ#XC%±–±—±˜±™±ž±Ÿ³‚±“Ò#XC%>Õ#XC%±™±ŸÒ#$U$1.it.Ñ$1 Periodic WavesÒ23$U$1.nxt.Ñ:GO: .zchl.ð±ðIntroduction to Periodic Waves±±µ†ŒµˆŒ˜ðDefinition of Periodic Waves±ðDefinition of a Sine Wave±ðDefinition of Wavelength±ðExample of Wavelength±ðExample of Wavelength±ðDefinition of Wave Frequency±± ðDefinition of Hertz± ðExample of Wave Frequency± ðIntroduction to Wave Velocity± ðDefinition of Wave Velocity± ðTest of Periodic Waves±Ò$Ð$UÒ/Ô$U500Ò<Ô$U500 mÒNÔ$U500 metersÒ`Ô$U500 metresÒtÔ$Ufive hundredÒÔ$Ufive hundred metresÒªÔ$Ufive hundred metersÒÂÔ$UIt is 500 metersÒÚÔ$UIt is 500 metresÒûÔ$UIt is five hundred metersÒÔ$UIt is five hundred metersÒAÔ$UThe wavelength is 500 meters*ÒfÔ$UThe wavelength is 500 metres*ÒyÔ$UIt is 500 mÒÔ$UIt is 500 m.Ò¬Ô$UThe wavelength is 500 mÒÌÔ$UThe wavelength is 500 m.±¬±•±«Õ#XC%±”ðReview of Periodic Waves±ðReview of Periodic Waves±ðIntroduction to Amplitude±ðDefinition of Amplitude±ðExample of Amplitude±±ðTest of Periodic Waves±Ò$j$UÒ-|$UbÒ6n$UaÒ?u$UcÒM|$Uline bÒ[n$Uline aÒiu$Uline cÒ€|$Uthe answer is bÒ—n$Uthe answer is aÒ®u$Uthe answer is cÒÊ|$Uthe answer is line bÒæn$Uthe answer is line aÒu$Uthe answer is line cÒ|$Uthe amplitude is bÒ;|$Uthe amplitude is line bÒf|$Uthe amplitude of the wave is line b±¬±±¬±›±¬±œ±«Õ#XC%±šðReview of Periodic Waves±ðReview of Periodic Waves±ðReview of Periodic Waves±ðReview of Periodic Waves±ðDefinition of the Period of a Wave±±±ðTest of Periodic Waves±Ò$z$UÒ6~$U1000 hertzÒP~$Uone thousand hertzÒ_~$U1000 HzÒv~$Uone thousand Hz±¬± ±«Õ#XC%±¡ðReview of Periodic Waves±ðReview of Periodic Waves±ðReviewñPress RETURN to continue, ? for help±±[±z± ±9Ò#XA%>Õ#XA%±B±J±Q±kÒ/6#XB%>Õ#XB%±u±“ÒHO#XC%>Õ#XC%±™±Ÿ± ²$ðPhysics Volume 2 Disk 1òType your answer and press RETURNñPress RETURN to continue, ? for helpÖ*"Ö*eÖ*ˆÖ*$Ö*&Ö*(Ö**Ö*,Ö*.Ö*†Ö#XAÖ#XBÖ#XC´ ´´´´´´´Z´y´´´ ´ ´ ±¦±¥ðñ±®ðPhysics Volume 2 Disk 1Ò5D#XA%>ÒAR#XA%>àcÔ$3masteryàqÔ$3needs workàqÔ$3incompleteÒ}Œ#XB%>Ò‰š#XB%>à«Ô$4masteryà¹Ô$4needs workà¹Ô$4incompleteÒÅÔ#XC%>ÒÑâ#XC%>àóÔ$5masteryàÔ$5needs workàÔ$5incomplete±!ðPhysics Volume 2 Disk 1±¯±´±ª±©ñ±µ±°±#±¶ðñ±·ðñ±¸À%You have completed À(%DISK 1.À@%If you wish you may review the material covered by typing REVIEW ALL or proceed to DISK 2. (À @%PROCEED TO DISK 2 À %Arrakis AdvantageÀ(%Developed byÀ 1%ARRAKIS SYSTEMS INC.À H%In co-operation withÀ Q%COLES THE BOOK PEOPLEÀp%Copyright 1986 by Arrakis Systems Inc. )À H% McGraw-Hill ÀX%presentsÀ h%Arrakis Advantage¡*À @%What do you mean?¡+À @%Undefined concept.À L%Please see overview.¡+À@%Not available for this concept.¡+À %The concepts coveredÿin this tutorial are presented in a predetermined order.À (%You may, however, interrupt the program AT ANY TIME to:À @%* ask questions * test your progress * review a concept * advance to a new conceptÀ q%question and press RETURN.À h%Just type your message or (¡,À%USE THESE WORDS TO:À%*ÿGo to another concept:À%goto, show me, teachÀ(%*ÿReview a concept:À0%review, review allÀ@%*ÿTest your progress:ÀH%score, testÀX%*ÿAsk questions:ÿdefine,À`%example, what isÀp%*ÿOther commands:ÿagain, overview,Àx%quit, repeat, restart, resume -À@%ÿCORRECT!¡.À=%ÿCORRECT!À=%IN¡/À@%CHARACTERISTICS OF LIGHT À0%Man has always known about light, but he has only thought about it scientifically for a relatively short time. 0À %We know that light travels FROM one place TO another. Prove it by putting your hand in front of a flashlight.ÿThere is a shadow on only one side. 1À%The Romans tried to measure theÀ %speed of light using lanterns andÀ0%hourglass timers.À@%But light travels at a rate ofÀP%3 ÀP&MÿÀP%1OÀ P'ÿÀ P%meters per second. ThisÀ`%was much too fast for theirÀp%instruments to measure. À %Medieval scholars thought that white light was pure and good and that colors were impure and bad. Sir Isaac Newton showed that white light was composed of all colors. 2À(%Here are some known facts about light. Any good theory of light will have to explain them all. À%Light usually travels in straight lines. This fact allows us to "line up" objects. 3À%However, lightÀ(%bends slightlyÀ8%lightÿÿÿÿÿÿÿÿÿÿÿÿÿÿwhen passingÀH%through glass.À X%ÿÿÿÿÿÿÿÿÿÿThis effect isÀh%called REFRACTION.ÀP%airÿÿÿÿairÀ`%glass 4À "%small opening. This effectÀ +%is called DIFFRACTION. YouÀ =%holding your fingers veryÀ F%close together and lookingÀ O%between them at a brightÀ X%object. The bending willÀ a%create a series ofÀ j%parallel dark lines.À %Light also bends whenÀ %it passes through a veryÀ 4%can see diffraction by 5À%Light reacts with different materials in different ways. A material may be TRANSPARENT, like glass, and allow light to pass through without breaking up or becoming disorganized. 6À%A material may be TRANSLUCENT, like waxed paper, and allow light to pass through, but not allow clear images to be seen.ÀP%Bathroom windows are sometimes made of translucent glass. 7ÀX%A material may be OPAQUE and block the passage of light completely.Àp%Wood is opaque. So are most other materials. 8À %If I look through a piece of material and see only a hazy outline of the objects on the other side, the material is:ÀP%1) transparentÀ`%2) translucentÀp%3) opaque 9À0%A translucentÿmaterial transmitsÀ@%light, but you can't see throughÀP%it. À (%Remember:À 8%You can see clearly through a transparent material. À(%Remember:À8%An opaque material blocks light completely. You can't see anything at all through it. À%Opaque materials cast a shadow. If the source of the light is small or far away, the shadow has quite sharp edges. :À%Opaque materials cast a shadow. If the source of the light is small or far away, the shadow has quite sharp edges. ;À%If the light source is large and relatively close, the shadow will be indistinct and blurred.ÀO%penumbraÀ\%umbra <À%The dark area in the center is completely hidden fromÿÿÿÿÿÿÿ the light source.À(%It is called the UMBRA.ÀT%umbra =À%The gray surrounding area is called the PENUMBRA.À %It receives light from some, but not all, of the light sources.ÀP%penumbra >À%If the light source is large and the object small, there will be no umbra.ÀZ% penumbra ?À%Name the area indicated. >À0%Remember:À@%The partly shaded area is the penumbra. À 8%The penumbra is theÀ D%partly shaded area. À%When light hits a transparent or translucent material, it passes right through. We say that these materials TRANSMIT light.ÀV%transmitted lightÀ y%À x% transparent @À%When lightÿhits a material it may be ABSORBED. A black surface absorbs light. AÀ %When light hits a material itÀ%may be REFLECTED. There are twoÀ%types of reflection. If theÀ(%surface is shiny, like a mirror,À1%the reflection is SPECULAR,À:%also known as REGULAR, (noticeÀx%mirror surfaceÀB%the equal angles of reflection). BÀ!%of white paper, the reflectionÀ%If light reflects from a pieceÀ*%is said to be DIFFUSE.Àx%white paper CÀ%In most cases, transmission,À % À%absorption, and reflectionÀ-%Consider anÀ4%ordinaryÀh%front ÿÿÿ backÀ u% mirrorÀ 5&À .%glassÀK& ÀK%shiny surfaceÀ<%mirror.ÀD% ÿThe shiny ÿsurface ÿis on the ÿback.À%occur in varying degrees at the same time. DÀ%When light strikes a mirror, some is reflected at the front surface. Most passes through the glass (some is absorbed), and most of what is left is reflected at the back surface.ÀP%someÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿmost reflected reflectionÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿsomeÀx%some absorbedÀp% most transmittedÀ8%frontÿÿbackÀ`%absorbed EÀ %Which is most prominent when light strikes a piece of glass?À8%1) transmissionÀH%2) reflectionÀX%3) absorption 9À 8%Remember:À H%Even though absorption and reflection do occur,À Y%most light is TRANSMITTED through a piece of glass. FÀ(%Transmission is most prominentÀ8%when light strikes a piece ofÀH%glass. À8%And now - some amazing facts about color! À%Materials seem to be colored because they reflect or transmit certain colors ofÀ0%greenÿÿÿÿÿÿÿÿÿÿÿÿlight.ÀH%This one simple theory states thatÀX%blueÿÿÿÿÿÿÿÿÿÿÿÿÿwhite light is madeÀ`%up of red, green,À%redÀ<&ÿÀ<%ÿ whiteÀh%and blue. GÀ%A red shirt is red because it reflects mostly red light.À$%If you shine a white light on it, the green and blue components will be absorbed.ÀH%whiteÀD%red reflectsÀ X%green and blue doÀ p%= red+green+blueÿÿÿÿÿnot HÀ%A piece of blue glass is blue because it transmits blue only, and not red or green.ÀB%blue transmittedÀH%whiteÀh%red and greenÿabsorbedÿ IÀ0%Tree leaves appear green when illuminated with white light because they absorb whichÿtwo colors? 9À %Remember:À0%White light is made up of red, green, and blue.ÀH%If you see green, the red and the blue must have been absorbed. À %REFRACTION:À0%The bending ofÀ@%lightÿÿÿÿÿÿÿÿÿÿÿÿÿÿlight or a waveÀ X%ÀP%airÿÿÿÿairÿÿÿÿwhen entering aÀ`%glassÿÿÿÿÿÿÿdifferent material. 4À %ABSORPTION:À%A material absorbs light if it neither reflects nor transmits light. JÀ%SPECULAR REFLECTION:À(%Mirror-like reflection of images.Àx%mirror surface BÀx%white paperÀ%DIFFUSE REFLECTION:À(%The type of scattered reflectionÀ8%that you get from a piece ofÀH%paper. CÀ @%NATURE OF WAVES ÀP%return to the study of light itself.À%Since the time of Newton, most of the characteristics of light have been explained by assuming that it is composed of very small waves,À(%something like water waves.À@%You will study waves for a while, then KÀ%A wave is a vibration that moves through or on a material.À%The material is called a MEDIUM.À(%Water WAVES travel on water. SoundÿWAVES travel through air. LÀ%A wave is a vibration that moves through or on a material.À%The material is called a MEDIUM.À(%Water WAVES travel on water. Sound WAVES travel through air. MÀ %Begin by looking at waves traveling along a linear object, like a piece ofÿÿ cord or a stretched spring. NÀ %Begin by looking at waves traveling along a linear object, like a piece ofÿÿ cord or a stretched spring. OÀ%A complete wave is called one CYCLE.À%The top of the wave is called a CRESTÀ %(sometimes a peak) and the bottom isÀ,%called a TROUGH (pronounced troff).ÀF%troughÀ9%crestÀx%one cycle PÀ5%Ocean waves often have whitecaps.ÀI%Do these occur at the crests or the troughs? 9À(%Whitecaps occur at the topsÀ8%of the waves. The tops areÀH%called crests, the bottomsÀX%are called troughs.À%Remember: À0%The whitecaps occur on theÀ@%tops of the waves, which areÀP%called the CRESTS.À %Right: À%A wave must always be in motion.À$%The direction in which a wave moves is called its DIRECTION OFÀ5%PROPAGATION.ÀH% direction ofÀP%propagation QÀ%Sometimes waves propagate inÀ&%only one direction. QÀ%They may also propagate in many directions at once.À(%  RÀ%They may also propagate in many directions at once.À(%  SÀ%They may also propagate in many directions at once.À(%Note the arrows showing the directions of propagation. TÀX%As a wave moves along a spring, some parts of the spring move up and other parts move down.À %motion of wave UÀX%As a wave moves along a spring, some parts of the spring move up and other parts move down.À%moving upÀ %motion of waveÀ@%moving down VÀ%When the direction of propagation of a wave is perpendicular to the motion of the medium in which it travels, the wave is said to be a TRANSVERSE WAVE.À8%motionÿÿÿmotion of waveÀ @%of medium WÀ@%It is also possible to send waves lengthwise along a spring. ÀX%Such a wave stretches certain parts of the spring and compresses others.À+%ÿÀ(%_______À 4%ÿmotion of wave XÀ@%It is also possible to send waves lengthwise along a spring. ÀX%Such a wave stretches certain parts of the spring and compresses others.À+%ÿÀ(%_______À 4%ÿmotion of wave YÀM%When the direction of propagation of a wave is parallel to the motion of the medium in which it travels, it is called a LONGITUDINAL WAVE.À %motion of waveÿÀ 0%motion of mediumÀ%LongitudinalÀ$%WaveÀ )&  XÀ0%TRANSVERSEÿWAVEÀD%LONGITUDINALÀL%WAVE ZÀ%Sound waves, which are vibrationsÀ(%in air, are longitudinal waves. MÀ%Imagine a wave moving on the water in a lake.À5%Are water wavesÀE%1) transverse 2) longitudinal 3) both transverse andÿlongitudinal 9À%Right!À-%The water surface moves up andÿdown, while the wave moves horizontally, so water waves are both transverse and longitudinal. However, they seem to move in a transverse direction. À%Remember:À-%The water surface moves up andÿdown, while the wave moves horizontally, so water waves are both transverse and longitudinal. However, they seem to move in a transverse direction. À0%PROPAGATION is the motion of a wave. À @%PERIODIC WAVES À%Up until now, you have studied single, isolated waves. In nature, waves occur more often as a continuous stream. À<%Single waves are highly unlikely occurances. [À%Up until now, you have studied single, isolated waves. In nature, waves occur more often as a continuous stream. À<%Single waves are highly unlikely occurances. \À%Waves usually occur as a series of identical crests and troughs.À$%They are spaced equally, and are about the same shape and height.À8%Such waves are called PERIODIC WAVES. ]À%Return to the example of the coil spring. You can send an identical series of waves along it.À0%The smooth shape shown here is special. Since it is the same shape as a sine graph in trigonometry, it is called a SINE wave. ^À%The distance between one wave and the next is called the WAVELENGTH. In physics, wavelength is indicated by the Greek letter ÿÿÿÿÿÿbda). TheÀ&À% (lamÀ'%diagram shows that wavelength can be measured from crest to crest, trough to trough or between any two identical points. _À,%The wavelength of waves on a lake can be a few centimeters. `ÀP%The wavelength of ocean waves can be several meters. aÀ%If you were to stand in a lake with a stopwatch, you could count the number of waves passing by in any given time interval.À,%The number of waves per unit time is called FREQUENCY.À@%Frequency is represented by the letter f. bÀ%If you were to stand in a lake with a stopwatch, you could count the number of waves passing by in any given time interval.À,%The number of waves per unit time is called FREQUENCY.À@%Frequency is represented by the letter f. cÀ%Frequency is usually measured in waves per second.À%One wave per second is called oneÀ%%HERTZ (abbreviated Hz) and is often written as secondsÿ (or sÿÀ,%-ÿÿÿÿÿÿÿ-À.%).Àx%one waveÀ@%1 secondÀ Z%inÿÿÿÿÿÿÿÿÿÿÿ= dÀ&ÿMÀ 'An AM radio station could broadcast using a frequency of 6.OO ÿ 1O Hz,À'or 6OO kilohertzÿ(6OO kHz). eÀ%If the water waves are O.5 m long and are going past you at the À%rate of 3 waves per second, it should be possible to figure out how fast they are going. À2%Think about it À:%ÿgo on and see if you were right.ÀH%3 waves/secondÀP%______À S%ÿÀ2%ÿfor a moment, thenÀF%O.5ÀN%m fÀ %If you guessed that they go 1.5 meters/second you are correct. The formula for finding the velocity v of a wave is: Àh%Velocity = frequency Àh&MÀh% wavelengthÀp%(lambda) gÀj'(Àj%GÀj'ive your answer in metersÀr%.)À&ÿMÀ&ÿMÀ 'If our radio station at 6OO kHz (6 ÿ 1O) sends out waves that travel at 3 ÿ 1O m/s, what is the wavelength of those waves? eÀW'3ÀW%(meters/second)À W&MÀ W'1Oÿm/sÀX'ÿ___________ÀF% À a&ÿMÀ`%ÿ-À`%(Hz)Ào'=ÿ5OOÿmÀW%ÿ ÿ ÀZ'=À8%À%You are right! Simply turn the formula around, and out pops the answer.Ào%ÿ ÿÿÿ Àa%6ÿÿÿ1OÀa'ÿÀa%sÿ hÀW'3ÀW%(meters/second)À W&MÀ W'1Oÿm/sÀX'ÿ___________ÀF% Àa%ÿ6ÿÀ a&ÿMÿÀ a%ÿ1OÀa'ÿÿÀa%ÿsÿÿÿÿÿ(Hz)À_%ÿ-Ào'=ÿ5OOÿmÀW%ÿ ÿ ÀZ'=À8%À%To get the correct wavelength, simply turn the formula around to solve for À&À%, as shown here.Ào%ÿ ÿÿÿ  hÀ%The next consideration is the height of the waves. Waves can be larger or smaller and still have the same wavelength and frequency. iÀ%The distance a wave moves the medium in which it travels away from center is called the AMPLITUDE of the wave. For physical waves, like water waves, it is measured in meters (from the crest or trough to the center) but for other waves, like electrical waves, it is measured in volts or whatever unit is appropriate.ÿÿÿÿÿÿÿÿÿÿÿaÀY%either "a" shows amplitudeÀ P%a jÀ%The amplitude of a light wave determines how bright the light is. The amplitude of a sound wave determines how loud the sound is. The amplitude of an electric wave might determine the strength of À7%an electric shock you get! kÀ%The amplitude of a light wave determines how bright the light is. The amplitude of a sound wave determines how loud the sound is. The amplitude of an electric wave might determine the strength of À7%an electric shock you get! lÀ%On this diagram, which line represents the amplitude of the wave?ÀO%AÀ?%CÀ H%B mÀ%Correct. Line B shows the amplitude, which is the distance from the center to either a crest or a trough.À H%BÀ?%CÀO%A nÀ %You have indicated that the amplitude goes from a crest to a trough. This is twice the correct value. The amplitude goes from the CENTER to either a crest or a trough, as shown by line B.À H%BÀ?%CÀO%A nÀ %The line you have picked represents the wavelength. The amplitude is correctly shown by line B, and isÿÿÿÿ the distance from the center to either a crest or a trough.À?%CÀO%AÀ H%B nÀ%Line B shows one amplitude, which is the distance from the center to either a crest or a trough.ÀO%AÀ?%CÀ H%B nÀ%Only one thing remains: the length of time it takes for one wave to pass. This time is called the PERIOD of the wave. Period is usually measured in seconds, and is represented by the letter T. bÀ%Only one thing remains: the length of time it takes for one wave to pass. This time is called the PERIOD of the wave. Period is usually measured in seconds, and is represented by the letter T. cÀ%You may have realized that period is closely related to frequency. In fact, period is simply the inverse of frequency.À H%Period = 1/frequencyÀX%ÿT = ÀT%ÿ1ÀU%ÿ_À^%ÿf À9%If a sound wave has a period of ÀD%1.O À D&M À D%1O  seconds, what is itsÀ B%-ÀO%frequency, in hertz? 9À%ÿAll you have to do is invert the period, as shown, to get the frequency. Incidentally, 1 is about the frequency of the tone À@%f = À<%ÿ1À=%ÿ_ÀF%ÿTÀX%ÿ= ÀU%ÿ___________À T%ÿ1À^%ÿ1.O À ^&ÿMÀ ^%ÿ1OÿÀ\%ÿ-Àm%ÿ= 1À %OOO HzÀ0%produced when you whistle.Àm%OOO sÿ or 1OOO HzÀ k%-À^% s À%Right. Frequency is the inverse of period, so just do as shown here.À %Incidentally, 1OOO Hz is about the frequency of the tone produced when you whistle.À@%f = À<%ÿ1À=%ÿ_ÀF%ÿTÀX%ÿ= ÀU%ÿ___________À T%ÿ1À^%ÿ1.O À ^&ÿMÀ ^%ÿ1OÿÀ\%ÿ-Àm%ÿ= 1À k%-Àm%OOO sÿ or 1OOO HzÀ^% s À 8%You will now returnÀ H%to the main path! À"%ÿ________________________________À %SCOREÀ %PHYSICS VOLUME 2À %Disk 1À=%of Lightÿÿÿÿÿÿÿÿÿÿ\$3ÀM%Nature of Wavesÿÿÿÿÿ\$4À5%CharacteristicsÀ]%Periodic Wavesÿÿÿÿÿÿ\$5 oÀ %ARRAKIS ADVANTAGEÀ0%PHYSICS Volume 2ÀP% ÀX%fromÀ h% McGRAW-HILL  pÀ %OVERVIEWÿÿÿÿÿÿÿÿÿÿDiskÿ1À %Here is what you will learn on this disk:À @%CHARACTERISTICS OFÿLIGHTÀ P%NATURE OF WAVESÀ `%PERIODIC WAVES ( 3336>   >>><<ÿÿçÃÃçÿÿ0<~00  $fÿf$<~ÿÿÿÿ~< 333?? >0 3 3 00 3;?73  ?303?30030333?00?00333?30 333333>0 0  0>> 0`0 30 333> 33?3333333333333?33??3333>333?333> >800033333333?!3??333337?;3333333333333833333303? 333333?33333 333??3!33 33333 ?3 3?< < 00<00000< 33ÿ 0>3>333300>33>3?333>0333 00033333 3?33333333333333>00330 ? 3333>333 333?33 3333>0? ?8  8  8 n;wQwÿ`6fp6> <<ÿÿçÃÃçÿÿ0 c3 fc 00 3;?73  ?303?30030333?00?00333?30 333333>0 0  0~~ 0`0 30 333> 33?3333333333333?33??3333>333?333 800033333333?!3??333337?;3333333333333833333303? 333333?33333 333??3!33 33333 ?3 3?< < 00<00000< 33ÿ 0>3>3333000>33>3?333>0333 00033333 3?33333333333333>00330 > 3333>333 333?33 3333>0~0 ~8  8  8 n;wQwÿ  ?0000~$$$$$ffÀ~gffffd$4,$&%<< ??@ ~ÿÙ½½™Ãÿffd$4,$&%ü ü þÆþÆÆæg ?  0 c0 `c 0<~~< <63þÛÛÞØØØ000 ?ÿ ? ? 00$fÿf$<~ÿÿÿÿ~<66666666 >0 c3 fc6n;3n    f<ÿ0 0  0`ÿÿ 0 ÿ>ckk{ 33?33~~3n>ff;33800>33n3?6n33>06nffg 000033f66g 3?3333333333;ff>n33>0x;nf>0 > ,3333n333 333?3c66c333>0? &?8  8 8 n;wQwÿ 333 6>>>  >>><<ÿÿçÃÃçÿÿ0? ?<~00  $fÿf$<~ÿÿÿÿ~< 333?? >0 3 30 0  0~~ 0`0 30 333> 33?3333333333333?33??3333>333?333 800033333333?!3??333337?;3333333333333833333303? 333333?33333 333??3!33 33333 ?3 3?< < 00<00000< 33ÿ 0>3>333300>33>3?333>0333 00033333 3?33333333333333>00330 ? 3333>333 333?33 3333>0? ?8  8  8 n;wQwÿ€–0`@#€—0` €qr0`1a@€qr…˜‘@` 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