Module 4 - Electrons, Waves and Photons

• Wave


  Transfer of energy from one place to another (not transfer any matter)
• Types of waves


  • Transverse
  • Longitudinal (Compression Waves)
• Transverse wave


  • Oscillations are perpendicular to the direction of energy transfer
• Longitudinal wave


  • Oscillations are parallel to the direction of energy transfer
• Example of Longitudinal waves

  • Sound waves
• Displacement


  Distance of one entire oscillation
• Amplitude


  Maximum displacement during an oscillation
• Time period


  Time it takes to complete one oscillation
• Frequency


  Number of oscillations per second (unit = Hz)
• Wave speed


  v = f x λ (wavelength)
• Example: Sound wave of 400 Hz and a wavelength of 70 cm, find its speed
• Progressive wave


  An oscillation that travels through a medium (or vacuum)
• Progressive waves


  • Particles in the medium move from their original equilibrium position to a new position
  • They exert forces on each other
• Standing/stationary wave


  Superposition of two progressive waves travelling in opposite directions, no energy transfer
• Reflection


  • Occurs when a wave changes direction at a boundary between two different media
  • Angle of incidence = angle of reflection
  • Wavelength and frequency remain the same
• Refraction


  Change in direction of a wave when it passes from one medium to another with a different refractive index
• Superposition


  Adding two waves together
• Oscillation


  A complete cycle of motion, which is then repeated
• Period


  Time for one oscillation
• Wavelength


  Distance travelled by a wave during one oscillation
• Phase shift


  Horizontal shift of a sine wave compared to a reference graph
• Refractive index


  Ratio of the speed of light in a vacuum to the speed of light in a medium
• Refractive index of air = 1, water = 1.3, glass = 1.5
• When a wave goes from a medium with lower refractive index to one with higher refractive index

  The angle of refraction decreases (bends towards the normal)
• Speed of sound in air varies with temperature
• Speed of a wave on a string

  Varies with tension, length and mass of the string
• Speed of water waves depends on water depth, surface tension and density
• Amplitude

  The maximum displacement of a wave from its equilibrium (rest) position. The height of the wave from the highest point (crest) to the lowest point (trough). Often used to describe the "size" of a wave and represented by the letter A.
• Wave

  Representation of a wave
• Time period

  Time it takes for one complete wave/cycle
• Frequency

  Reciprocal of the time period
• Radians

  Unit of angle measurement, 2π radians = 1 full circle
• Waves

  • Full wave = 2π radians
  • Half wave = π radians
  • Quarter wave = π/2 radians
  • Eighth wave = π/4 radians
• Phase difference

  Difference in the position of two waves, can be measured in radians or degrees
• Finding phase difference

  1. Take 2π

  2. Multiply by time difference between two points

  3. Divide by time period

  4. Or take 2π

  5. Divide distance between two points

  6. Divide by wavelength
• Superposition of waves


  • Waves interfere and superimpose
  • Constructive interference at peaks and troughs
  • Destructive interference at nodes
• Standing wave

  Stationary wave formed by two identical waves travelling in opposite directions
• Standing wave

  • Nodes - zero amplitude
  • Anti-nodes - maximum amplitude
• Fundamental mode


  Simplest standing wave, half wavelength
• Harmonics

  • Higher frequency standing waves, integer multiples of fundamental frequency
  • Overtones - higher harmonics heard faintly with fundamental