Waves and quantum behaviour

• Antiphase

  When two waves are at opposite positions (eg. one is at a peak and the other is at a trough), they are in antiphase
• Phase


  The stage in the wave cycle
• Wave Properties

  • Wavelength: the distance, in metres, between equivalent points on two consecutive waves (eg. peak to peak or trough to trough)
  • Displacement: the distance from equilibrium position. The maximum displacement is known as the amplitude
  • Frequency: the number of complete waves passing a given point in one second
  • Time period: the time taken for a wave to completely pass through any given point. This is the reciprocal of the frequency: 1/time period = frequency & 1/frequency = time period
• Out of phase


  When two waves are not in phase or antiphase
• Phase difference calculation

  Can be worked out using phasor arrows, which rotate 360 degrees in the time it takes for a wave to complete a full cycle. 360° is equal to 2π radians. Radians are commonly used to describe phasors. Resultant phasors can be worked out in the same way as resultant vectors - scale arrows are drawn tip to tail, and then connected by a resultant arrow. The angle can be measured from a scale drawing
• Path difference

  The difference between the distance travelled by two waves when they meet. A path difference that is a whole number multiple of the wavelength (n λ) produces waves in phase. A path difference of (n +1/2)of the wavelength produces waves in antiphase. Anything in between produces waves that are out of phase
• Coherent waves

  Waves that have a constant phase difference
• In phase


  When two waves are at the same point at the same time, they are in phase
• Light can be modelled as discrete packages of energy called photons
• Absolute refractive index


  The ratio of the speed of light in a material to the speed of light in a vacuum
• Refraction is the change in speed of a wave (eg. light) when it reaches a boundary between two media
• The energy of a photon of light depends on its frequency
• Refractive index

  The ratio of the speed of light in two different materials
• Working out the speed of sound in air

  1. Use a resonance tube partially submerged in water

  2. Hold a tuning fork over the top and move the tube up and down until resonance occurs, producing a louder sound

  3. Measure the length required to produce the first resonance

  4. Repeat for the second resonance
• Photon


  Carries a fixed quantity of energy called a quanta
• Nodes

  Always form at closed ends
• Sound waves travel along a tube

  1. Reflect at the end of the tube

  2. Waves travel up and down the tube and superimpose
• Huygens’ wavelet model


  Helps to explain refraction by describing a wave of light as being made up of many smaller wavelets
• Diffraction is the spreading out of waves when they pass through a gap of roughly the same width as their wavelength
• Diffraction gratings have multiple slits and work similarly to double slits
• The energy of waves is normally a very small quantity, so the electronvolt unit is used
• Antinodes


  Always form at open ends
• Snell’s law relates the refractive index to the angles of incidence and refraction
• Young’s double slit experiment

  Light passes through two small slits and spreads out, producing a pattern of light (antinodes) and dark (nodes) fringes on a screen
• The photoelectric effect occurs when light is incident on the surface of a metal and quantas of energy carried by photons are absorbed
• 1 electronvolt is equal to 1.6 x 10^-19 Joules
• Single slit diffraction produces the same interference effect and can be explained by Huygens’ wavelet model
• Work function (Φ)

  The amount of energy required to liberate electrons from the surface of the metal
• The de Broglie equation provides a way to calculate the wavelength of electrons: λ = h / mv
• LEDs rely on the photoelectric effect and can be used to determine Planck’s constant
• Energy of emitted electrons

  Depends on the frequency of the light, with higher frequency light resulting in higher energy photoelectrons
• Quantum model of light

  The quantum behaviour of light models a ray of light as taking every possible path between where it is emitted and detected
• If the frequency is below the threshold frequency, no electrons will be emitted
• More intense light does not change the energy of the electrons but means that more electrons are emitted
• 1eV = 1.6 x 10^-19 J
• Photoelectric effect


  Occurs when light is incident on the surface of a metal, causing electrons to move up to a higher energy level or be liberated from the surface
• Intensity

  The amount of energy per second per unit area
• Electron diffraction


  Electrons diffract in the same way as light to produce diffraction patterns, showing wave behaviour
• Maximum energy of emitted electrons calculation

  E = hf - Φ
• Intensity

  Proportional to the square of the length of the resultant phasor