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  1. 1. Vibrations & Waves
  2. 2. 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.
  3. 3. 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.
  4. 4. 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.
  5. 5. 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.
  6. 6. 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.
  7. 7. Transverse Waves Stretched strings in a musical instrument ocean waves, radio and lightare all examples of transverse waves.
  8. 8. Transverse WavesTransverse Wave
  9. 9. 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.
  10. 10. 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.
  11. 11. Longitudinal Waves As the wave particles set neighbouring particles into motion the wave is propagated through the medium, energy is transferred in the medium.
  12. 12. Longitudinal Waves Wavelength of a longitudinal wave distance between successive compressions or successive rarefactions.
  13. 13. 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.
  14. 14. Defining Terms Displacement:  The distance a particle has moved from its mean position.
  15. 15. Defining Terms Crest:  Positive displacement of a transverse wave. Trough:  Negative displacement of a transverse wave.
  16. 16. Defining Terms
  17. 17. 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.
  18. 18. Defining Terms
  19. 19. Defining Terms
  20. 20. 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.
  21. 21. Defining Terms
  22. 22. Defining Terms Amplitude:  The difference between the maximum displacement and the mean position.  Symbol A  Unit (SI) metre.
  23. 23. Defining Terms
  24. 24. Defining Terms Period:  The time for one complete oscillation.  Symbol T  Unit (SI) second.
  25. 25. Defining Terms Frequency:  Is the number of wavelengths generated by a source in a second.  Symbol f  Unit (SI) Hertz (Hz)
  26. 26. Defining Terms Frequency and period are related by the formula; 1 f T
  27. 27. 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.
  28. 28. 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.
  29. 29. 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
  30. 30. 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 ?
  31. 31. Sound barrier
  32. 32. 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.
  33. 33. 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.
  34. 34. 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.
  35. 35. 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)
  36. 36. 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.
  37. 37. Graphical Representation of Waves
  38. 38. Graphical Representation of Waves
  39. 39. 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.
  40. 40. 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.
  41. 41. Reflections in one Dimension Reflection from a boundary
  42. 42. Reflection From a Fixed End
  43. 43. 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.
  44. 44. 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.
  45. 45. Reflection From a Free End
  46. 46. 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.
  47. 47. 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
  48. 48. Reflections in one Dimension
  49. 49. Partial Reflection from a Heavier Spring lighter spring . heavier spring . . .
  50. 50. 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.
  51. 51. Reflections in one Dimension Two pulses of reduced amplitude move at speeds characteristic of the media result.
  52. 52. Partial Reflection From a Lighter Spring .
  53. 53. 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.
  54. 54. 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.
  55. 55. 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.
  56. 56. 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.
  57. 57. Reflections in Two Dimensions
  58. 58. 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
  59. 59. 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.
  60. 60. 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.
  61. 61. 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.
  62. 62. Reflection
  63. 63. Reflection
  64. 64. Reflection When the mirror is curved sizes & distances of the object and image, are no longer equal, but the law of reflection still holds.
  65. 65. Reflection
  66. 66. Reflection
  67. 67. Reflection Concave Mirror
  68. 68. 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.
  69. 69. Reflection Reflection of Light
  70. 70. Reflection
  71. 71. 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
  72. 72. 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.
  73. 73. Criteria for Interference in 2 D
  74. 74. 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.
  75. 75. Criteria for Interference in 2 D Mutually coherent wave sources maintain a constant phase relationship.
  76. 76. Criteria for Interference in 2 D
  77. 77. 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
  78. 78. 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,........
  79. 79. 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
  80. 80. 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.
  81. 81. 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.
  82. 82. Refraction of Waves in 1 & 2 Dimensions
  83. 83. Refraction of Waves in 1 & 2 Dimensions
  84. 84. 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.
  85. 85. Refraction of Waves in 1 & 2 Dimensions
  86. 86. Refraction of Waves in 1 & 2 Dimensions i = angle of incidence R = angle of refraction D = angle of deviation
  87. 87. 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.
  88. 88. Refraction of Waves in 1 & 2 Dimensions
  89. 89. 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
  90. 90. Refraction
  91. 91. Refraction
  92. 92. 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.
  93. 93. Refraction Waves can also be refracted in air. This can happen when winds are uneven or, when sound travels through air, of uneven temperature.
  94. 94. Refraction
  95. 95. Refraction
  96. 96. Total Internal Reflection Beam of light travelling through water hits a water/air interface. Some light is refracted some reflected.
  97. 97. 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.
  98. 98. Total Internal Reflection At angles greater than ic no light is refracted, it is totally internally reflected.
  99. 99. Total Internal Reflection o air R R=90water i r ic
  100. 100. 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.
  101. 101. Applications This allows the light to be channelled around corners, used by anyone from mechanics, to doctors and dentists.
  102. 102. 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.