Waves

• Progressive wave


  Transfers energy from one place to another
• Types of progressive waves

  • Transverse wave
  • Longitudinal wave
• Transverse wave


  • Particles oscillate perpendicular to the direction of propagation of the wave or the direction of energy transfer
  • Examples include water waves, EM waves
• Longitudinal wave


  • Particles oscillate parallel to the direction of propagation of the wave or the direction of energy transfer
  • Examples include sound waves, P-waves in earthquakes
• Displacement


  Distance from a point in the wave to the equilibrium
• Amplitude


  Maximum displacement from a point of the wave to the equilibrium position
• Wavelength


  Minimum distance between two points in phase
• Time period


  Time taken for one complete oscillation
• Frequency


  Number of cycles per unit time, measured in Hertz (cycles per second)
• Time period


  Inversely proportional to frequency
• Wave speed


  Distance traveled by the wave per unit time
• Phase difference


  How far out of sync two points on a wave are
• If two waves differ by 180°, they differ by half a wavelength
• Oscilloscope


  Horizontal axis represents time, vertical axis represents voltage
• Reflection


  • Wave changes direction but remains in the original boundary
  • Angle of incidence = Angle of reflection
• Refraction


  • Wave changes direction and speed as it moves from one medium to another
  • Frequency remains constant, speed and wavelength change
• Diffraction


  • Spreading of a wave as it passes through a gap or around an obstacle
  • Gap size needs to be similar to the wavelength
• Intensity


  Power transmitted per unit area, measured in W/m^2
• Intensity and distance from source


  I ∝ 1/r^2
• Intensity and amplitude


  I ∝ A^2
• Electromagnetic waves


  • Can travel through a vacuum
  • Travel at the speed of light (3.0 x 10^8 m/s)
  • Transverse waves with oscillating electric and magnetic fields
• Electromagnetic spectrum


  • Radio waves
  • Microwaves
  • Infrared
  • Visible light
  • Ultraviolet
  • X-rays
  • Gamma rays
• Plane polarized wave


  Particles/fields oscillate in a single plane
• Unpolarized light


  Particles/fields oscillate in multiple directions
• Wavelength ranges


  • 4 x 10^-7 to 2 x 10^-8 m (x-rays)
  • -10 to -10^-10 m (gamma rays)
  • Smallest observed around 10^-16 m
• Plane polarized wave


  Electromagnetic fields oscillating in a single plane
• Unpolarized light


  Oscillating in multiple directions (vertical, horizontal, etc.)
• Vertically polarized light


  Represented by double arrow
• Horizontally polarized light


  Represented by horizontal arrow
• Longitudinal waves cannot be polarized
• Using polarizing filters


  1. Light passes through first filter, absorbing one polarization

  2. Second filter absorbs the remaining polarization, blocking all light
• Refractive index


  Ratio of speed of light in vacuum to speed of light in a substance
• Refractive index has no units
• Calculating speed of light in a substance


  Speed of light in vacuum / Refractive index
• Light going from lower to higher refractive index

  Bends towards the normal
• Light going from higher to lower refractive index

  Bends away from the normal
• Using Snell's law to calculate angle of refraction

  1. n1 sin(theta1) = n2 sin(theta2)

  2. Rearrange to find theta2
• Measuring refractive index experimentally

  1. Vary angle of incidence, measure angle of refraction

  2. Plot graph of sin(theta1) vs sin(theta2)

  3. Gradient is the refractive index
• Total internal reflection


  Occurs when light goes from higher to lower refractive index, and angle of incidence is greater than critical angle
• Calculating critical angle


  sin(critical angle) = 1 / refractive index