Waves

• Progressive wave


  Transfers energy without transferring material, made up of particles of a medium (or field) oscillating
• Progressive wave


  • Amplitude
  • Frequency
  • Wavelength
  • Speed
  • Phase
  • Phase difference
  • Period
• Amplitude


  Wave's maximum displacement from the equilibrium position
• Frequency


  Number of complete oscillations passing through a point per second
• Wavelength

  Length of one whole oscillation
• Speed

  Distance travelled by the wave per unit time
• Phase


  Position of a certain point on a wave cycle
• Phase difference


  How much a particle/wave lags behind another particle/wave
• Period


  Time taken for one full oscillation
• Two points on a wave are in phase if they are both at the same point of the wave cycle, they will have the same displacement and velocity and their phase difference will be a multiple of 360 degrees(2π radians), they do not need the same amplitude, only the same frequency and wavelength
• Two points are completely out of phase when they're an odd integer of half cycles apart e.g. 5 half cycles apart where one half cycle is 180° (π radians)
• Transverse wave


  Oscillation of particles (or fields) is at right angles to the direction of energy transfer
• Transverse waves


  • Electromagnetic (EM) waves
  • Waves seen on a string
• Longitudinal wave


  Oscillation of particles is parallel to the direction of energy transfer, made up of compressions and rarefactions
• Longitudinal waves


  • Sound
• Polarised wave


  Oscillates in only one plane
• Polarisation provides evidence for the nature of transverse waves because polarisation can only occur if a wave's oscillations are perpendicular to its direction of travel
• Applications of polarisation


  • Polaroid sunglasses
  • TV and radio signals
• Superposition


  Displacements of two waves are combined as they pass each other, the resultant displacement is the vector sum of each wave's displacement
• Constructive interference


  Occurs when 2 waves have displacement in the same direction
• Destructive interference


  Occurs when one wave has positive displacement and the other has negative displacement, if the waves have equal but opposite displacements, total destructive interference occurs
• Stationary wave


  Formed from the superposition of 2 progressive waves, travelling in opposite directions in the same plane, with the same frequency, wavelength and amplitude. No energy is transferred.
• Where the waves meet in phase, constructive interference occurs so antinodes are formed, which are regions of maximum amplitude. Where the waves meet completely out of phase, destructive interference occurs and nodes are formed, which are regions of no displacement.
• Formation of stationary wave on a string


  1. Wave travelling down the string from the oscillator

  2. Wave reflected at the fixed end

  3. Superposition of the two waves
• First harmonic


  Lowest frequency at which a stationary wave forms, with two nodes and a single antinode
• You can double the first harmonic frequency to find the second harmonic where there are 2 antinodes, you triple the first harmonic frequency to get the third harmonic where there are 3 antinodes, and so on for the nth harmonic
• Examples of stationary waves

  • Stationary microwaves
  • Stationary sound waves
• Path difference


  Difference in the distance travelled by two waves
• Coherent light source


  Has the same frequency and wavelength and a constant phase difference
• Examples of coherent light sources

  • Lasers
• Young's double slit experiment

  1. Shine a coherent light source through 2 slits

  2. Each slit acts as a coherent point source making a pattern of light and dark fringes

  3. Light fringes are formed where the light meets in phase and interferes constructively

  4. Dark fringes are formed where the light meets completely out of phase and interferes destructively
• Using white light instead of monochromatic laser light gives wider maxima and a less intense diffraction pattern with a central white fringe with alternating bright fringes which are spectra, violet is closest to the central maximum and red furthest
• Lasers can permanently damage your eyesight therefore, when using lasers there are several safety precautions, which must be followed
• Evidence for the wave nature of light was provided by Young's double slit experiment because diffraction and interference are wave properties, and so proved that EM radiation must act as a wave (at least some of the time)
• Diffraction


  Spreading out of waves when they pass through or around a gap
• The greatest diffraction occurs when the gap is the same size as the wavelength. When the gap is smaller than the wavelength most waves are reflected, whereas when it is larger there is less noticeable diffraction. When a wave meets an obstacle you get diffraction round the edges, the wider the obstacle compared to the wavelength, the less diffraction
• Monochromatic light can be diffracted through a single slit onto a screen, which forms an interference pattern of light and dark fringes. The pattern has a bright central fringe, which is double the width of all other fringes, with alternating dark and bright fringes on either side, the bright fringes are caused by constructive interference where the waves meet in phase and the dark fringes are caused by destructive interference where waves arrive completely out of phase
• Diffraction


  The spreading out of waves when they pass through or around a gap
• Diffraction


  • The greatest diffraction occurs when the gap is the same size as the wavelength
  • When the gap is smaller than the wavelength most waves are reflected
  • When the gap is larger there is less noticeable diffraction
  • When a wave meets an obstacle you get diffraction round the edges, the wider the obstacle compared to the wavelength, the less diffraction
• Diffraction of monochromatic light through a single slit

  1. Forms an interference pattern of light and dark fringes

  2. Bright central fringe is double the width of all other fringes

  3. Alternating bright and dark fringes caused by constructive and destructive interference

  4. Intensity of fringes decreases from central fringe