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Waves. Waves revision. Watch a “Mexican Wave”. Some definitions…. 1) Amplitude – this is “how high” the wave is:. 2) Wavelength ( ) – this is the distance between two corresponding points on the wave and is measured in metres:.
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Waves revision Watch a “Mexican Wave”
Some definitions… 1) Amplitude – this is “how high” the wave is: 2)Wavelength ()– this is the distance between two corresponding points on the wave and is measured in metres: 3) Frequency – this is how many waves pass by every second and is measured in Hertz (Hz)
Transverse vs. longitudinal waves Displacement Direction Direction Displacement Transverse waves are when the displacement is at right angles to the direction of the wave… Longitudinal waves are when the displacement is parallel to the direction of the wave… Where are the compressions and rarefactions?
Oscillating Systems l g T = 2π m k T = 2π Design an experiment that determines what the period of oscillation depends on for these two oscillating systems:
Displacement-time graphs “Sinusoidal” Equilibrium position Displacement Time Consider a pendulum bob: Let’s draw a graph of displacement against time:
Phase Difference There is a ‘phase difference’ between two waves when they have the same frequency but oscillate differently to each other. For example: These two waves have different amplitudes but the same frequency and hit their peaks at the same time – they are “in phase” These two waves start opposite to each other – they are “in antiphase” or “out of phase by π radians”
Phase Difference What is the phase difference between each of these waves?
The Wave Equation V f The wave equation relates the speed of the wave to its frequency and wavelength: Wave speed (v) = frequency (f) x wavelength () in ms-1 in Hz in m
Some example wave equation questions • A water wave has a frequency of 2Hz and a wavelength of 0.3m. How fast is it moving? • A water wave travels through a pond with a speed of 1ms-1 and a frequency of 5Hz. What is the wavelength of the waves? • The speed of sound is 330ms-1 (in air). When Dave hears this sound his ear vibrates 660 times a second. What was the wavelength of the sound? • Purple light has a wavelength of around 6x10-7m and a frequency of 5x1014Hz. What is the speed of purple light? 0.6ms-1 0.2m 0.5m 3x108ms-1
Electromagnetic Radiation E-M radiation is basically a movement of energy in the form of a wave. Some examples:
The Electromagnetic Spectrum High frequency, _____ wavelength Low frequency, _____ (high) wavelength γ Each type of radiation shown in the electromagnetic spectrum has a different wavelength and a different frequency: Each of these types travels at the same speed through a _______ (300,000,000ms-1), and different wavelengths are absorbed by different surfaces (e.g. infra red is absorbed very well by ___________ surfaces). This absorption may heat the material up (like infra red and _______) or cause an alternating current (like in a __ _______). Words – black, microwaves, long, short, TV aerial, vacuum
The Electromagnetic Spectrum Type of radiation Uses Dangers Treating cancer, sterilisation Gamma rays Cell mutation X rays Medical Cell mutation Ultra violet Sun beds Skin cancer None (unless you look at the sun) Visible light Seeing things Remote controls, heat transfer Infra red Sunburn Microwaves Satellites, phones Very few TV/radio Communications Very few
Water Waves Q. Design an experiment that explores the relationship between the depth of water and the speed of a wave in that water.
Reflection revision Normal Reflection from a mirror: Reflected ray Incident ray Angle of reflection Angle of incidence Mirror
Refraction through a glass block Light slows down and bends towards the normal due to entering a more dense medium Light speeds up and bends away from the normal due to entering a less dense medium Light slows down but is not bent, due to entering along the normal
Refractive Index v1 v2 Speed in medium 1 1μ2 = Refractive index = Speed in medium 2 sinθ1 sinθ2 sin i sinr 1μ2 = = Willebrord Snellius, 1580-1626 The Refractive Index of a material is a measure of the factor by which the material will slow down light: Using some interesting maths I turned this relationship into Snell’s Law:
Questions on the Refractive Index Air • Calculate the angles θW and θG for light incident at 40O to the air-water boundary: Water Glass The speed of light is 3x108ms-1 in air, 2.3x108ms-1 in water and 2x108ms-1 in glass. • Calculate the refractive index for light passing from air into water, from air into glass and from water into glass.
More Questions… My law can often be stated as this: μ1 sin θ1 = μ2 sin θ2 1) Light passes from water (refractive index of 1.3) into crystal with a refractive index of 1.5. Calculate the angles of refraction for light incident at 20O, 30O, 40O and 50O. 2) A ray of light travels through a vacuum and is incident upon a glass block (of refractive index 1.5) at an angle of 30O. The ray then passes into water. Draw an accurate diagram to show the path of this light as it travels from the vacuum through the glass and into the water.
Measuring the Refractive Index Sin i sinθ1 sinθ2 sin i sinr 1μ2 = = Sin r Using Snell’s Law we can measure the refractive index of a material: From this equation a graph of sin i against sin r will have a gradient of the refractive index:
Finding the Critical Angle… THE CRITICAL ANGLE 1) Ray gets refracted 2) Ray still gets refracted 4) Ray gets internally reflected 3) Ray still gets refracted (just!)
Uses of Total Internal Reflection Optical fibres: An optical fibre is a long, thin, _______ rod made of glass or plastic. Light is _______ reflected from one end to the other, making it possible to send ____ chunks of information Optical fibres can be used for _________ by sending electrical signals through the cable. The main advantage of this is a reduced ______ loss. Words – communications, internally, large, transparent, signal
Polarisation Consider a single wave of light: If you looked at it “end on” it might look like this: And lots of them might look like this:
Polarisation and Microwaves Describe an experiment that demonstrates that microwaves are polarised.
Sugar Solution and Polarised Light Task: To investigate the amount of sugar dissolved in a solution using polarised light. Method: • Measure and dissolve 10g, 20g, 30g, 40g and 50g of sugar into 100ml of water • Investigate the angle of rotation needed to block out a light source using the solution and two polaroid filters • Draw a graph of angle against concentration • Use this graph to determine the amount of sugar in unknown solution x.
Pulse-Echo techniques In pulse-echo techniques sound is reflected from an object to measure the distance to that object:
Pulse-Echo techniques - Ultrasound Ultrasound is the region of sound above 20,000Hz – it can’t be heard by humans. It can be used in pre-natal scanning: How does it work? Ultrasonic waves are partly _________ at the boundary as they pass from one _______ to another. The time taken for these reflections can be used to measure the _______ of the reflecting surface and this information is used to build up a __________ of the object. Words – depth, reflected, picture, medium
The Maths of Pulse-Echo x Consider shouting at a wall: The speed of sound is given by: v = 2x/t Therefore x = vt/2
The Maths of Pulse-Echo 25 50 75 100 125 150 175 200 t/μs The echo takes 0.8 seconds to return and the speed of sound in water is 1500ms-1. How deep is the water? Use the ultrasound scan to determine the width of the amniotic sac and the width of the baby’s body. The speed of sound in the fluid is 1500ms-1 and in soft tissue the speed is 1560ms-1.
Ultrasound vs X Rays • Why are X Rays better than ultrasound? • Why is ultrasound better than X Rays?
Phase Difference Revision Phase difference means when waves have the same frequency but oscillate differently to each other. For example: These two waves have different amplitudes but the same frequency and hit their peaks at the same time – they are “in phase” These two waves start opposite to each other – they are “in antiphase” or “out of phase by π radians”
Coherence Two waves are said to be “coherent” if they have the same frequency and the same constant phase difference. For example: These waves have a different frequency, so phase is irrelevant.
Coherence These waves have the same frequency and the same constant phase difference, so they are “coherent”
Superposition Superposition is seen when two waves of the same type cross. It is defined as “the vector sum of the two displacements of each wave”:
Superposition patterns Consider two point sources (e.g. two dippers or a barrier with two holes): Stable interference patterns happen when these waves are the same type, coherent AND have similar amplitudes at the point of supperposition.
Path Difference 1st Max Min Max Min 1st Max Constructive interference Destructive interference 2nd Max
Young’s Double Slit Experiment D λ s O x x D xs D λ s λ = = Screen A
Interference Patterns from 2 slits Intensity Distance
Interferometers Task: Find out what an interferometer is. Include the following: • Where they are used • A diagram of how they are used • Some pictures • The physics principle behind how they work (i.e. the use of a path difference)
How CD Players work Path difference between these two waves = 0, therefore constructive interference Path difference between these two waves = λ/2, therefore destructive interference λ/4 Silvery surface CDs are made of millions of small bumps etched onto a silvery surface using a laser. Here’s how they work:
Stationary (Standing) Waves Usually waves are described as “travelling” or “progressive” waves, i.e. there is a net movement of energy. However, it is possible to set up a standing wave using two progressive waves of equal frequency and wavelength: This is hard to imagine, but if you put these two waves together you’d get this:
Stationary (Standing) Waves 3 nodes 2 antinodes 5 nodes 4 antinodes
Harmonics l Fundamental frequency f0, λ=2l First overtone, second harmonic, f=2f0, λ=l Third overtone, fourth harmonic, f=4f0, λ=l/2
