03: Waves

• Progressive wave


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


  • Wave's maximum displacement from the equilibrium position (units are m)

  
• Frequency, f


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


  • 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


  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)
• In phase


  Two points on a wave are at the same point of the wave cycle, have the same displacement and velocity, and their phase difference is a multiple of 360° (2π radians)

  
• Completely out of phase

  Two points are an odd integer of half cycles apart (e.g. 5 half cycles apart where one half cycle is 180° (π radians))
• Wave speed, c


  Equal to the wave's frequency multiplied by its wavelength: c = f/λ

  
• Frequency, f


  Equal to 1 over its period: f = 1/T
• Transverse waves


  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 attached to a signal generator

  
• Longitudinal waves


  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 waves

  
• Polarised wave


  Oscillates in only one plane (e.g. only up and down), only transverse waves can be polarised

  
• Polarised waves


  • 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

  
• Antinodes


  Regions of maximum amplitude where the waves meet in phase and constructive interference occurs

  
• Nodes


  Regions of no displacement where the waves meet completely out of phase and destructive interference occurs

  
• First harmonic frequency


  Lowest frequency at which a stationary wave forms, with two nodes and a single antinode, distance between adjacent nodes (or antinodes) is half a wavelength

  
• Higher harmonic frequencies


  Double, triple, etc. the first harmonic frequency to get 2, 3, etc. antinodes
• 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
• Coherent light sources


  • Lasers
• Young's double slit experiment

  Shine a coherent light source through 2 slits about the same size as the wavelength, each slit acts as a coherent point source making a pattern of light and dark fringes

  
• Fringe spacing, w


  w = sλ/D, where s is slit separation, λ is wavelength, and D is distance between screen and slits

  
• White light interference


  Gives wider maxima and a less intense diffraction pattern with a central white fringe and alternating bright fringes which are spectra, violet closest to central maximum and red furthest

  
• Lasers can permanently damage eyesight, so safety precautions must be followed when using them
• Interference in sound waves

  • Use two speakers connected to the same signal generator, measure intensity with a microphone to find maxima and minima

  
• Young's double slit experiment provided evidence for the wave nature of light, as diffraction and interference are wave properties

  
• Diffraction


  Spreading out of waves when they pass through or around a gap, greatest when gap is same size as wavelength

  
• Diffraction and gap size

  Waves are reflected when gap is smaller than wavelength, less diffraction when gap is larger than wavelength

  
• Diffraction and obstacle size


  Less diffraction when obstacle is wider compared to the wavelength
• Monochromatic light diffraction


  Forms an interference pattern of light and dark fringes, with a bright central fringe double the width of other fringes