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 = fλ
• Wave frequency, f


  f = 1/T
• Transverse wave


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

  
• All electromagnetic (EM) waves are transverse and travel at 3 x 10^8 ms^-1 in a vacuum
• Transverse waves

  • Shaking a slinky vertically
  • 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
• Longitudinal waves are made up of compressions and rarefactions and can't travel in a vacuum
• Longitudinal waves


  • Sound
  • Pushing a slinky horizontally
• Polarised wave


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

  
• 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 (as they are in transverse waves)
• Applications of polarisation


  • Polaroid sunglasses
  • TV and radio signals
• Superposition


  The 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
• 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
• Formation of stationary waves

  • A string fixed at one end, and fixed to a driving oscillator at the other
• 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
• Distance between adjacent nodes (or antinodes)

  Half a wavelength (for any harmonic)
• 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


  The difference in the distance travelled by two waves
• Coherent light source


  Has the same frequency and wavelength and a fixed phase difference

  
• Lasers are an example of light which is coherent and monochromatic, meaning they emit a single (or small range of) wavelength(s) of light
• Young's double slit experiment

  Demonstrates interference of light from two-sources
• Young's double slit experiment

  1. Shine a coherent light source through 2 slits about the same size as the wavelength of the laser light so the light diffracts

  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, this occurs where the path difference between waves is a whole number of wavelengths (nλ, where n is an integer)

  4. Dark fringes are formed where the light meets completely out of phase and interferes destructively, this occurs where the path difference is a whole number and a half wavelengths ((n+½)λ)

  
• 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