Waves

• Transverse waves

  • particles move perpendicular to the motion of travel (up and down)
  • electromagnetic spectrum is An example

  Longitudinal waves

  • particles move parallel to the motion of travel (back and forth)
  • examples include ultrasound and sound

  
• Refraction - where waves change direction as it enters a different medium with changing densities
• Diffraction - when a wave moves through a gap

  • If the wavelength is equal (~) to the gap size, the wave shall spread out in all directions
  • if the gap is larger than the wavelength, the wave doesn’t spread out as much (this is the reason why sound diffracts but light doesn’t - light has a smaller wavelength)

  
• Polarisation only occurs with transverse waves

  
• Sin(I) is proportional to sin(r)

  Therefore sin(I)/sin(r) give us constant n (Snell‘s law)

  N is also speed in air (I) / speed in r (glass)

  
• Critical angle and TIR

  • TIR = total internal reflection where light is refracted 100% of the glass

  When light goes glass > air:

  • as r shall be > I, if we increase I to make r = 90 degrees, it’ll travel across the boundary at 90 degrees (critical angle)
  • If I is higher and causes an angle > critical angle, the reflected light shall be TIR

  Let N = refractive index of a material / air

  • Sin C (sin critical angle) = N(air) / N(glass)

  
• If light is travelling from air to glass:

  • Light shall move slower when in the glass
  • Therefore as wave speed in decreasing and frequency is constant, wavelength has to decrease (C = f x lamda)
• Fibre optics:

  • Angle of R must exceed critical angle for TIR
  • therefore N1 > N2
  • To stop chances of light patterns becoming ”loose”, make the ”cylinder” in which light in N1 is in super small
• Superposition

  • when two waves meet and the total displacement = sum of each of the individual waves’ displacement
  • Constructive = in phase
  • Destructive = out of phase

  
• Interference = when two coherent waves pass through each other
• Coherent = waves with constant phase different, amplitude and same wavelength
• Phase differerence = fraction of a cycle between two particles oscillating on a wave (deg and rad)
• Path difference - same as phase difference but measured in metres or fraction of wavelength

  • Destructive and constructive interference
• Two sources of interference:

  • two waves shall create points of constructive and destructive interference

  
• Young’s double slit experiment:

  • a = slit separation - distance between the slits
  • D = distance between slit and whiteboard (where laser ends up)
  • x = fringe separation - distance between each fringe (measure 10 then divide by 10 for 1)

  wavelength = ax/d

  other:

  intensity of light is shown through lazer focus areas

  
• Diffraction gratings:

  • dsin(theta) = wavelength x n
  • where d = distance between slits (says on diffracting grating)
  • n = order of the maxima

  Each maxima goes 0th maxima, 1st order, 2nd order, etc

  To calculate d:

  • create right angled triangle with distance between grating + board against distance between an order

  Sin(theta) is proportional to the wavelength

  • if sin(theta) increases, the wavelength increases too

  
• Stationary waves on a string:

  • weight maintains tension on string as string oscillates due to changed frequency
  • only progressive waves (oscillations transferring energy from one place to another). Progressive w hits end and creates stationary wave
  • Wave reflects at the end
  • as Frequency increases, more standing waves

  Node = no displacement

  Anti node = point of maximum displacement

  As frequency increases, wavelength decreases

  
• Stationary waves:

  • where energy is stored
  • formed when progressive wave hits boundary and reflects. This interaction causes a stationary wave. Will have same amplitude and phase difference

  Fundamental frequency = frequency for first standing wave to be made

  
• Stationary wave in a partially open column:

  • one end is open so anti node and one side is closed so node
  • 1st harmonic has a wavelength of 1/4 As node > anti node = 1/4
  • 2nd harmonic you had node > node so add 1/2 wavelength

  
• Stationary wave in an open column:

  • always starts and ends with an antinode
  • 1st harmonic = 1/2 wavelength
  • 2nd harmonic = 1/2 + 1/2 = 1 wavelength