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Waves
 

Waves

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    Waves Waves Presentation Transcript

    • Vibrations & Waves
    • WAVES Energy can be transferred in a number of ways. A moving car is an example of energy in motion Not only does the energy move the car moves as well. Energy can move without the object/particle moving with it. This occurs in waves.
    • Travelling WaveCharacteristics A surfer;  sitting on their board,  waiting for the right wave. While waiting;  ocean waves pass under him,  while he bobs up and down. Flick a slinky spring;  wave passes along the slinky while,  particles move up and down.
    • Travelling WaveCharacteristics Drop a stone in a still pond;  you produce a wave that moves out from the centre,  in ever increasing circles. Check the water before and after the wave passes,  You find that the water,  remained where it was.
    • Travelling WaveCharacteristics In these examples the particles vibrate or oscillate. The wave has been transferred without a transfer of matter. The signals from radio and T.V.’s are waves. Sound and light travel as waves.
    • Transverse Waves If you create a wave by shaking a slinky up and down, the motion of the medium is at right angles to the motion of the wave. This type of wave is called a transverse wave.
    • Transverse Waves Stretched strings in a musical instrument ocean waves, radio and lightare all examples of transverse waves.
    • Transverse WavesTransverse Wave
    • Longitudinal Waves When the particles of the medium move in the same direction as the wave, it is known as a longitudinal wave. They are less common. Sound travels as a longitudinal wave.
    • Longitudinal Waves In both forms, the energy can be transferred as a single pulse, a number of pulses, or a continuous wave. Particles may be set in motion by a wave no particle travels far from its initial position.
    • Longitudinal Waves As the wave particles set neighbouring particles into motion the wave is propagated through the medium, energy is transferred in the medium.
    • Longitudinal Waves Wavelength of a longitudinal wave distance between successive compressions or successive rarefactions.
    • Defining Terms Medium:  The substance through which the wave moves the particles making up the medium, are those which are displaced, as the wave moves through it.
    • Defining Terms Displacement:  The distance a particle has moved from its mean position.
    • Defining Terms Crest:  Positive displacement of a transverse wave. Trough:  Negative displacement of a transverse wave.
    • Defining Terms
    • Defining Terms Compression:  Regions of a longitudinal wave that;  have a high density of particles. Rarefaction:  Regions of a longitudinal wave that;  have a low density of particles.
    • Defining Terms
    • Defining Terms
    • Defining Terms Wavelength:  The distance covered in a complete wave cycle.  The distance between two consecutive points in phase.  Symbol Greek letter  Unit (SI) metre.
    • Defining Terms
    • Defining Terms Amplitude:  The difference between the maximum displacement and the mean position.  Symbol A  Unit (SI) metre.
    • Defining Terms
    • Defining Terms Period:  The time for one complete oscillation.  Symbol T  Unit (SI) second.
    • Defining Terms Frequency:  Is the number of wavelengths generated by a source in a second.  Symbol f  Unit (SI) Hertz (Hz)
    • Defining Terms Frequency and period are related by the formula; 1 f T
    • Defining Terms Wave Speed:  Is the speed at which a given point on the wave, is travelling through the medium.  The product of frequency and wavelength. Mathematically represented by v =f Unit (SI) ms-1.
    • Defining Terms Characteristic of the medium the wave travels through. Sound waves in air typically 330 ms-1 to 350 ms-1 depending on the density of the air and four times faster in water.
    • SoundSound is a longitudinal wave, but it’s speed depends on the medium Sound in a solid Sound in a gas Pulse of sound Sound in a bell jar Different atmosphere music playing
    • Speed of sound calculations What is the speed of sound for each of these: 1. Travels 127m in 0.1 sec 2. Travels 1608 m in 4 sec 3. Travels 1493 cm in 0.01 sec 4. Travels 120km in 10 secWhich answer is speed of sound in water, air, diamond ?
    • Sound barrier
    • Sound barrier As an airplane approaches the speed of sound, shock waves build up, creating increase in drag, loss of lift, and loss of control. When travelling near the speed of sound, the plane came up against a "sound barrier"--as though the velocity of sound represented a wall through which a plane could not move. The sound barrier was broken in 1947.
    • Shock waves As an airplane flies faster than the speed of sound, it "pushes" on the sound waves in front of it. They continue to travel at the same speed. The waves pile up against each other as they are created. These are called shock waves.
    • Sonic Booms The shock waves will move out and back from the plane, towards the ground. There is a sudden change in pressure when the shock wave hits your eardrum. You hear this as a loud sonic boom.
    • Summary of Wave Speeds WAVE TYPE MEDIUM SPEED (ms-1) Sound Carbon Dioxide 260 Air 331 Hydrogen 1290 Pure Water 1410 Sea Water 1450 Glass 5500 Light Vacuum 2.997 x 108 Air 2.998 x 108 Glass (crown) 2.0 x 108 Earthquake Crust 3500 (transverse) 8000 (longitudinal) Mantle 6500 (transverse) 11000 (longitudinal)
    • The Behaviour of Waves When a wave moves through a medium the velocity and shape of that wave, remains constant. This is so, no matter what the medium.
    • Graphical Representation of Waves
    • Graphical Representation of Waves
    • Reflections in one Dimension When a wave reaches a boundary between two media some or all of the wave bounces back, into the first medium.
    • Reflections in one Dimension A pulse is sent along a slinky spring which is attached at one end to a wall. All the energy is reflected back along the spring, rather than into the wall.
    • Reflections in one Dimension Reflection from a boundary
    • Reflection From a Fixed End
    • Reflections in one Dimension The pulse becomes inverted as it is reflected. This is called phase reversal. This is why metals are so shiny. A Metal surface is rigid to the light waves that shine upon it.
    • Reflections in one Dimension Most of the light is reflected apart from a small energy loss, due to the friction of, the vibrating electrons in the surface. Metals can be used as mirrors for this reason.
    • Reflection From a Free End
    • Reflections in one Dimension The part of the spring adjacent to the boundary is free to be displaced, and no phase change occurs on reflection.
    • Reflections in one Dimension If the wall is replaced with a heavy spring as a new medium, some energy is transmitted, some energy is reflected. Reflection from a boundary
    • Reflections in one Dimension
    • Partial Reflection from a Heavier Spring lighter spring . heavier spring . . .
    • Reflections in one Dimension The heavy spring acts as an imperfect ‘rigid’ boundary, partially reflecting the pulse, with a change of phase but, also partially transmitting it.
    • Reflections in one Dimension Two pulses of reduced amplitude move at speeds characteristic of the media result.
    • Partial Reflection From a Lighter Spring .
    • Reflections in one Dimension The lighter spring acts as an imperfect ‘free end’, partially reflecting the pulse, without change of phase and, partially transmitting it. Two pulses with reduced amplitude are produced.
    • Reflections in Two Dimensions In one dimension the reflected wave simply travels back, in the direction from which it came. In two dimensions, the situation is a little different.
    • Reflections in Two Dimensions Direction of incident & reflected waves described by straight lines called rays. The incoming ray (incident ray) and the reflected ray makes, equal angles with the normal.
    • Reflections in Two Dimensions Angle between incident ray & normal called the angle of incidence Angle between the reflected ray & normal called the angle of reflection.
    • Reflections in Two Dimensions
    • Reflections in Two Dimensions Relationship is called Law of reflection. Law applies equally to both partially reflected and, totally reflected waves. Stated mathematically: i= r Reflection of light
    • Reflection If a lit candle is placed in front of a plane mirror, rays of light are reflected in all directions. There are an infinite number all obey the law of reflection.
    • Reflection The rays diverge from the tip of the flame and continue to diverge upon reflection. These rays appear to originate from a point located behind the mirror.
    • Reflection This is called a virtual image the light does not actually pass through the image, but behaves as though it virtually did. The image appears as far behind the mirror as the object is in front of it and, the object and the image is the same.
    • Reflection
    • Reflection
    • Reflection When the mirror is curved sizes & distances of the object and image, are no longer equal, but the law of reflection still holds.
    • Reflection
    • Reflection
    • Reflection Concave Mirror
    • Reflection For a rough surface each individual ray obeys the law of reflection many different angles light rays encounter in striking a rough surface cause, reflection in many directions. This is called diffuse reflection.
    • Reflection Reflection of Light
    • Reflection
    • Diffraction Diffraction is the spreading out of a wave as it passes through a gap. ƛ = d waves spread out ƛ < d no change to wave
    • Criteria for Interference in 2 D Consider a ripple tank with two dippers producing waves, of the same frequency and in phase. A two dimensional standing wave would be seen.
    • Criteria for Interference in 2 D
    • Criteria for Interference in 2 D Even if the dippers were out of phase by radians ( /2), the 2D standing wave pattern would still be seen. In both cases, the dippers maintain a constant phase relationship, referred to as mutually coherent sources.
    • Criteria for Interference in 2 D Mutually coherent wave sources maintain a constant phase relationship.
    • Criteria for Interference in 2 D
    • Criteria for Interference in 2 D For a point to be on a nodal line difference between its distance, from one source and the other source, called the geometric path difference, G.P.D. must be an odd number of half wavelengths. In the diagram above
    • Criteria for Interference in 2 D For any point on an antinodal line G.P.D. must be an even number of /2. This means that reinforcement occurs when G.P.D. = m , m = 0,1,2,........
    • Criteria for Interference in 2 DPhase relationship Annulment Reinforcementin phase G.P.D. = (2m+1) /2 G.P.D. = mphase reversal of one wave G.P.D. = m G.P.D. = (2m+1) /2phase reversal of both waves G.P.D. = (2m+1) /2 G.P.D. = m
    • Refraction of Waves in 1 & 2 Dimensions Place a pencil in a glass of water it appears bent, at the air/water interface. Bending or change in direction that occurs at the boundary, of two different media is called refraction.
    • Refraction of Waves in 1 & 2 Dimensions Place coin on bottom of empty coffee mug. Position yourself so the coin is just out of view the coin becomes visible as water is added. The coin still appears to be on the bottom the image of the coin and the bottom of the mug, must have moved up.
    • Refraction of Waves in 1 & 2 Dimensions
    • Refraction of Waves in 1 & 2 Dimensions
    • Refraction of Waves in 1 & 2 Dimensions Water in a pond appears to be only ¾ its true depth. The depth an object appears to be is called the apparent depth while its true depth is called, the real depth.
    • Refraction of Waves in 1 & 2 Dimensions
    • Refraction of Waves in 1 & 2 Dimensions i = angle of incidence R = angle of refraction D = angle of deviation
    • Refraction of Waves in 1 & 2 Dimensions Angle of refraction is less than angle of incidence when the 2nd medium is more optically dense than the first medium, such as when light travels from air to glass. This is reversed when light travels from glass to air.
    • Refraction of Waves in 1 & 2 Dimensions
    • Refraction of Waves in 1 & 2 Dimensions Light bends towards the normal when it enters a more optically dense medium. Light bends away from the normal when it enters a less optically dense medium. The amount the incident ray is deviated depends on the nature of the transparent material
    • Refraction
    • Refraction
    • Refraction As the waves move more slowly in shallow water the crests are closer together. Diagram above each line represents a crest, called a wavefront.
    • Refraction Waves can also be refracted in air. This can happen when winds are uneven or, when sound travels through air, of uneven temperature.
    • Refraction
    • Refraction
    • Total Internal Reflection Beam of light travelling through water hits a water/air interface. Some light is refracted some reflected.
    • Total Internal Reflection As i increases the amount of reflected light increases. At the critical angle, (ic) the light is moving at right angles, to the normal.
    • Total Internal Reflection At angles greater than ic no light is refracted, it is totally internally reflected.
    • Total Internal Reflection o air R R=90water i r ic
    • Applications Optical fibre cable is a strand of glass with a protective coating. The angle of incidence of the light is greater than the critical angle, so all light is reflected.
    • Applications This allows the light to be channelled around corners, used by anyone from mechanics, to doctors and dentists.
    • Applications Communications can also take advantage of this phenomenon. Copper cables carry information as electrical voltages, while optical cables can carry many messages, as modulations of laser light in binary signals,(‘on’ or ‘off’) at more than 40 million pulses a second.