Transcript Slide 1
4 Waves G482 Electricity, Waves & Photons 2.4.1 Wave Motion 2.4.2. EM Waves 2.4.3 Interference 2.4.4 Stationary Waves Mr Powell 2012 Index Introduction The module begins by reviewing and consolidating students’ prior knowledge about waves and wave properties. This is followed by a short section on electromagnetic waves also reinforcing and amplifying prior knowledge of the electromagnetic spectrum. Students then gain an understanding of superposition effects. The wavelength of light is too small to be measured directly using a ruler; however, experiments can be done in the laboratory to determine wavelength of visible light using a laser and a double slit. The module concludes by considering stationary waves formed on strings and in pipes. There are opportunities to discuss how theories and models develop with the Young’s double-slit experiment. The dangers of over-exposure to ultraviolet radiation are well known. This module explores which type of ultraviolet radiation is most dangerous to us and illustrates how scientific knowledge can be used to reduce risks for society. Mr Powell 2012 Index Practical Skills are assessed using OCR set tasks. The practical work suggested below may be carried out as part of skill development. Centres are not required to carry out all of these experiments. Students should gain a qualitative understanding of superposition effects together with confidence in handling experimental data. Students should be able to discuss superposition effects and perform experiments leading to measurements of wavelength and wave velocity. Use an oscilloscope to determine the frequency of sound. Observe polarising effects using microwaves and light. Investigate polarised light when reflected from glass or light from LCD displays. Study diffraction by a slit using laser light. Study hearing superposition using a signal generator and two loudspeakers. Study superposition of microwaves. Determine the wavelength of laser light with a double-slit. Determine the wavelength of light from an LED using a diffraction grating. Demonstrate stationary waves using a slinky spring, tubes and microwaves. Determine the speed of sound in air by formation of stationary waves in a resonance tube. Mr Powell 2012 Index 2.4.1 Wave Motion (Part A) Assessable learning outcomes... (a) describe and distinguish between progressive longitudinal and transverse waves; d (b) define and use the terms displacement, amplitude, wavelength, period, phase difference, frequency and speed of a wave; (c) derive from the definitions of speed, frequency and wavelength, the wave equation v = f; (d) select and use the wave equation v = f; (e) explain what is meant by reflection, refraction and diffraction of waves such as sound and light. Mr Powell 2012 Index (a) describe and distinguish between progressive longitudinal and transverse waves: Using a slinky you can try this out. In fact we are modelling how the air molecules compress and expand when we talk. VIBRATION Rarefaction is an expansion! Try it with a slinky! • Common examples:- Sound, slinky springs seismic p waves • Longitudinal waves cannot be polarised Mr Powell 2012 Index (a) describe and distinguish between progressive longitudinal and transverse waves: Direction of travel VIBRATION • The direction of vibration of the particles is parallel to the direction in which the wave travels. • Common examples:- Sound, slinky springs seismic p waves • Longitudinal waves cannot be polarised Mr Powell 2012 Index 6 (a) describe and distinguish between progressive longitudinal and transverse waves: Direction of travel vibration • The direction of vibration of the particles is perpendicular to the direction in which the wave travels. • Common examples:- Water, electromagnetic, ropes, seismic s waves • You can prove that you have a transverse wave if you can polarise the wave (especially important with light (electromagnetic) as you cannot “see” the wave!!) Try it with a slinky! Mr Powell 2012 Index 7 Exam Question…. (Basic Level) (a) State the characteristic features of (i) longitudinal waves, ............................................................................................................................ ............................................................................................................................ ............................................................................................................................ ............................................................................................................................ (ii) transverse waves. ............................................................................................................................ ............................................................................................................................ ............................................................................................................................ ............................................................................................................................ (3) Mr Powell 2012 Index Exam Question…. (Basic Level) (a) State the characteristic features of (i) longitudinal waves, ............................................................................................................................ ............................................................................................................................ (ii) transverse waves. ............................................................................................................................ ............................................................................................................................ (3) Answer a) (i) particle vibration (or disturbance or oscillation) (1) same as (or parallel to) direction of propagation (or energy transfer) (1) (ii) (particle vibration) perpendicular to direction of propagation (or energy transfer) (1) Mr Powell 2012 Index Mr Powell 2012 Index Mr Powell 2012 Index What is missing? Mr Powell 2012 Index (b) Measuring Waves Create a small summary for each of these key terms. Define what is means and draw a diagram to support your notes… Use page138 to assist you… Displacement Wave speed Amplitude Measuring Waves Frequency Wavelength Cycle / Period Wiki Mr Powell 2012 Index (b) Key Summary… Mr Powell 2012 Index (b) Timings? Q. A mains transformer vibrates the floor at 50Hz. What is the time for a complete cycle? 360 o = 2 radians Mr Powell 2012 Index (c) derive from the definitions of speed, frequency and wavelength, the wave equation v = f; speed = distance time Mr Powell 2012 Index (c) derive from the definitions of speed, frequency and wavelength, the wave equation v = f; Mr Powell 2012 Index (d) select and use the wave equation v = f; (i) Define the terms wavelength, frequency and speed used to describe a progressive wave (3 marks) (ii) Hence derive the wave equation v = fλ which relates these terms together. (2 marks) Mr Powell 2012 Index (d) select and use the wave equation v = f; (i) Define the terms wavelength, frequency and speed used to describe a progressive wave (3 marks) (ii) Hence derive the wave equation v = fλ which relates these terms together. (2 marks) (i) λ distance between (neighbouring) identical points/points with same phase (on the wave) accept peak/crest to peak/crest, etc.0 f number of waves passing a point /cycles/vibrations (at a point) per unit time/second accept number of waves produced by the wave source per unit time/second v distance travelled by the wave (energy) per unit time/second not v = f λ and not ‘in one second’ (ii )in 1 second f waves are produced each of one wavelength λ accept time for one λ to pass is 1/f so v = λ/(1/f) =f λ distance travelled by first wave in one second is f λ = v give max 1 mark for plausible derivations purely in terms of algebra (no words) Mr Powell 2012 Index (b) Phase Difference • These two waves are not “coherent” • What we are saying is all the peaks don’t match at the same time. • They have a “phase difference” 360 2 shift 2 • We can express this quite simply as a 2d time shift or distance shift. shift d d • If we are talking about a distance shift then a circle or cycle has 2 radians or 360 to return to the start. Shift = 360 * (60mm/240mm) = 90 or T or • We can express the shift as a Shift = 2* (60mm/240mm) fraction of the circle/ cycle where = 1.572 radians is a whole cycle and d is the shift or… Wiki NB: it often helps to think of waves as cycles or a clock face and two hands with a distance (or angle between them) d Mr Powell 2012 Index (b) Phase difference examples… Mr Powell 2012 Index (b) Lissajou Figures… (Extension) If we try using an Oscilloscope to show the idea we can plot two inputs against each other to form a dynamic graph. Input 1 = x, Input 2 = y Mr Powell 2012 Index Plenary Question…. What is the phase shift in degrees for these waves if… 1) d = 0.1m, = 1.2m 2) d = 22mm, , = 1.2m 3) Harder. Now repeat for radians. d Mr Powell 2012 Index Phase Shift Question…. What is the phase shift in degrees for these waves if… 1) d = 0.1m, = 1.2m 2) d = 22mm, , = 1.2m 3) Harder. Now repeat for radians. 1) Shift = 360 * (0.1m/1.2m) = 30 d 360 o = 2) Shift = 360 * (22 x 10-3m/1.2m) = 6.6 360 2 3) shift 2 = 0.52 radians = 0.12 radians shift 2d 2 radians d Mr Powell 2012 Index 2.4.1 Wave Motion (Part B) Assessable learning outcomes... (d) select and use the wave equation v = f; (e) explain what is meant by reflection, refraction and diffraction of waves such as sound and light. Be able to clearly explain the concept and features of… Reflection off a plane surface (water / light waves) (Basic) Refraction at a boundary (water / light waves slow in shallow) (Basic) Diffraction more for narrow gap or longer (water waves) Mr Powell 2012 Index Wave behaviour? Shouting around a corner? Mirrors Wavespeed Fuzzy edges on a shadow Wavefronts Water waves slow down in the shallows Light slows down in a medium Wavelength Mr Powell 2012 Index Key Points Refraction…. Waves pass a boundary i.e. air to glass prism or deep to shallow water they “refract” or change direction and change speed. Light bends in towards the normal for air to glass and reverse as it comes out. Water waves moving into the shallows slow down and have smaller . c= f so if c so Reflection…. Hard surface, angle incident = angle reflection (from normal). If water waves the fronts act at 90 to the direction of travel Diffraction…. Wave fronts incident on a gap. The narrower the gap the more the waves curve or the longer/larger the wavelength the more they spread out. Video Mr Powell 2012 Index Virtual Ripple Tanks… Use the virtual ripple tank here to explore wave properties. http://www.falstad.com/ripple/ Use the ideas from the book on page 179 and also you can download the additional information sheet on the blog to help you explore the ideas. Make summary notes on what you find for each situation. You may decide to screenshot out the image to help you. (NB: pick a nice colour scheme) W:\Students Read Only\Physics\AS\Unit 12\ripple tank\index.html Mr Powell 2012 Index Mr Powell 2012 Index Mr Powell 2012 Index Plenary Question. 1) Name one example each of reflection, refraction, and diffraction. (3 marks) a) Reflection: b) Refraction: c) Diffraction: 2) Then go on to explain at least 1 key feature of the Physics related to the process for each. (3marks) Reflection: Mirror surface, light travels at constant speed but changes direction on impact Refraction: Light enters a glass prism which is more dense than air so slows down (smaller wavelength) and changes direction (bends towards the normal) Diffraction: Water passes through a gap in a concrete bridge causing a circular wave front. The longer the wavelength (or smaller the gap) the more it spreads out. Mr Powell 2012 Index Connection • • • Connect your learning to the content of the lesson Share the process by which the learning will actually take place Explore the outcomes of the learning, emphasising why this will be beneficial for the learner Demonstration • Use formative feedback – Assessment for Learning • Vary the groupings within the classroom for the purpose of learning – individual; pair; group/team; friendship; teacher selected; single sex; mixed sex • Offer different ways for the students to demonstrate their understanding • Allow the students to “show off” their learning Activation Consolidation • Construct problem-solving challenges for the students • Use a multi-sensory approach – VAK • Promote a language of learning to enable the students to talk about their progress or obstacles to it • Learning as an active process, so the students aren’t passive receptors • Structure active reflection on the lesson content and the process of learning • Seek transfer between “subjects” • Review the learning from this lesson and preview the learning for the next • Promote ways in which the students will remember • A “news broadcast” approach to learning Mr Powell 2012 Index Extension Materials – Snells Law Θ1 = angle of incidence Θ2 = angle of refraction Incident ray 1 sin 1 1 n2 sin 2 normal 1 2 2 Refracted ray 1. The incident ray, the refracted ray and the normal all lie in the same plane. 2. For two given media, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant. Mr Powell 2012 Index Material Vacuum Air @ STP Gases @ 0 °C and 1 atm Air Carbon dioxide Liquids @ 20 °C Water Arsenic trisulfide and sulfur in methylene iodide Solids @ room temperature Diamond Strontium titanate Amber λ (nm) n 1 (per definition) 1.000277 589.29 589.29 1.000293 1.00045 589.29 1.3330 1.9 589.29 589.29 589.29 2.419 2.41 1.55 Water ice 1.31 cornea (human) 1.3375 Mr Powell 2012 Index What happens? air glass / water Mr Powell 2012 Index Explaining it... REFRACTIVE INDEX FROM 1 TO 2 c1 1 n2 c2 Optically less dense medium (1) Optically denser medium (2) c1 f1 1 1 n2 c2 f2 2 Waves travel SLOWER Wavelength REDUCED Frequency UNCHANGED NB: If c = f if speed is less as light finds it harder to get through glass the must go down as well Mr Powell 2012 Index Problem drawn out... If we try and think about the problem by drawing out the wave front and looking at triangles.. Then considering the constant velocity of the wave which then changes to a new constant velocity. Mr Powell 2012 Index Refraction - Triangles again... ct=YY’ i ct sin i XY ' XY’ cst=XX’ XY’ r ct XY ' sin i cs t sin r XY ' Think about how the wave slows when it reaches the medium. We can express the distance it travels YY’ or XX’ simply by s/v=t (constant vel) cs t XY ' sin r ct XY ' sin i cs t XY ' sin r c sin i cs sin r sin i ns sin r Then similar triangles result in a sin function for the angle calculations and an expression for a ratio of velocities. Finally we can express this ratio as what we call a refractive index or “how much the light slows down”. Higher is slower! Mr Powell 2012 Index Speed of Light... The speed of light, usually denoted by c, is a physical constant, so named because it is the speed at which light and all other electromagnetic radiation travels in vacuum. Its value is exactly 299,792,458 ms-1 The speed at which light propagates through transparent materials, such as glass or air, is less than c. The ratio between c and the speed v at which light travels in a material is called the refractive index n of the material (n = c / v). For example, for visible light the refractive index of glass is typically around 1.5, meaning that light in glass travels at c / 1.5 ≈ 200,000 km/s; the refractive index of air for visible light is about 1.0003, so the speed of light in air is very close to c. Wavelength REDUCED Waves travel SLOWER Frequency UNCHANGED Mr Powell 2012 Index Equilateral Prisms Sometimes it is better to think of Snells law as... Where you have two mediums. It does not matter which way they are around or what they are as long as you plug in the refractive mediums number. The equation simplifies to n = 1 for air. For an equilateral prism you can use this construct to work out the refraction as unlike a rectangular prism i1 i2 In essence what we mean is that every angle of reflection & refraction is different for the double refraction in an equilateral prism. You have to draw it out to work it out. n1 sin 2 n2 sin 1 Hint: 1. Draw a scale diagram 5cm each side. 2. 60 angles. 3. First refracted angle Measure........ 4. Measure 2nd incident ..... 5. Calc 2nd refracted ....... 6. What is n2 = Mr Powell 2012 Index Exam Question... Jan 2012 Mr Powell 2012 Index Exam Question... Jan 2012 Mr Powell 2012 Index Homework Q2 extra help.... = 1cm = 0.01m Gap = 0.75cm = 0.75 = 1cm = 0.01m Gap = 5.2cm = 5.2 = 0.052m Mr Powell 2012 Index