Waves

• Progressive wave

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

  • Amplitude
  • Frequency, f
  • Wavelength, λ
  • Speed, c
  • Phase
  • Phase difference
  • Period, T
• Amplitude

  A wave's maximum displacement from the equilibrium position (units are m)
• Frequency, f

  The number of complete oscillations passing through a point per second (units are Hz)
• Wavelength, λ

  The length of one whole oscillation (e.g. the distance between successive peaks/troughs) (units are m)
• Speed, c

  Distance travelled by the wave per unit time (units are m/s)
• Phase

  The position of a certain point on a wave cycle (units are radians, degrees or fractions of a cycle)
• Phase difference

  How much a particle/wave lags behind another particle/wave (units are radians, degrees or fractions of a cycle)
• Period, T

  Time taken for one full oscillation (units are s)
• 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° (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)
• Wave speed, c

  c = f * λ
• Frequency, f

  f = 1/T
• Transverse wave

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

  • All electromagnetic (EM) waves
  • Waves seen on a string, when it's attached to a signal generator
• Longitudinal wave

  Oscillation of particles is parallel to the direction of energy transfer, made up of compressions and rarefactions, can't travel in a vacuum
• Longitudinal waves

  • Sound
• Polarised wave

  Oscillates in only one plane (e.g only up and down), only transverse waves can be polarised
• 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 by a stationary wave
• Antinode

  Region of maximum amplitude where waves meet in phase, constructive interference occurs
• Node

  Region of no displacement where waves meet completely out of phase, destructive interference occurs
• The lowest frequency at which a stationary wave forms is the first harmonic, which forms a stationary wave with two nodes and a single antinode
• First harmonic frequency

  f = (1/2π) * √(T/μL)
• The distance between adjacent nodes (or antinodes) is half a wavelength (for any 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 fixed phase difference
• Examples of coherent light sources

  • Lasers
• Young's double slit experiment

  Demonstrates interference of light from two-sources
• Fringe spacing, w


  w = (λD)/s
• 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
• 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 a wave meets an obstacle you get diffraction round the edges, the wider the obstacle compared to the wavelength, the less diffraction