waves

• Waves are vibrations that transfer energy without matter
• Electromagnetic waves


  Oscillating electric and magnetic fields which progress through space without the need for a substance
• Electromagnetic spectrum


  • Radiowaves
  • Microwaves
  • Infrared radiation
  • Visible light
  • Ultraviolet
  • X-rays
  • Gamma rays
• Longitudinal waves


  Oscillate in the same direction
• Transverse waves


  Oscillate at 90 degrees to the direction of travel
• Displacement


  Distance from the undisturbed position
• Amplitude


  Maximum displacement from the undisturbed position
• Wavelength


  The distance between two corresponding parts of a wave
• Frequency


  Number of complete waves passing a point per second
• Period


  The time for one complete wave to pass a fixed point
• Wavespeed


  Frequency multiplied by wavelength
• Phase of a vibrating particle


  The fraction of a cycle it has completed since the start of the cycle
• Phase difference between 2 particles vibrating at the same frequency

  The fraction of a cycle between the vibrations of the 2 particles
• 1 cycle is equal to 360 degrees or 2 pi radians
• Intensity


  Amount of energy
• Units for


  • Wavelength: metres
  • Displacement: metres
  • Period: seconds
  • Frequency: Hertz
• Mechanical waves need particles to transfer energy and are created by physical oscillations of matter
• Longitudinal waves are always mechanical
• Electromagnetic waves do not need particles to transfer energy
• Plane-polarised


  Vibrations stay on one plane only
• Evidence for the nature of transverse waves is polarisation
• Transverse waves can be plane-polarised by passing them through a narrow slit
• If a 2nd slit is placed at 90 degrees to the 1st, it will block all wave energy from passing
• Plane of polarisation of an electromagnetic wave


  The plane in which the electric field oscillates
• Light from a lamp is unpolarised
• Use of polarisation includes polarised sunglasses to remove glare and polaroid filters to allow light to move in one direction only
• Applications of polarisers include the alignment of aerials for transmission and reception
• Principle of superposition


  When 2 waves meet, the total displacement at a point is equal to the sum of the individual displacements at that point
• Formation of stationary waves occurs when two or more progressive waves of the same frequency, travelling in opposite directions pass through each other
• Formation of stationary waves on a string
• Formation of stationary waves

  1. When two or more progressive waves of the same frequency, travelling in opposite directions pass through each other

  2. Fix both ends & make the string vibrate. Progressive waves travel towards each end, reflect at the ends, and then pass through each other to form a stationary wave

  3. Sound waves in a pipe reflect at the ends & the reflected waves pass through each other. In a pipe closed at one end, resonance occurs if there is an antinode at the open end and a node at the closed end

  4. Microwaves form a stationary pattern when they are reflected by a metal plate back towards the transmitter. When a detector is moved between the transmitter and metal plate, the detector signal is least at the nodes
• Stationary waves in tubes

  • One open end: node at closed end, antinode at open end
  • Both ends open: Antinode at each end
• Wave harmonics


  1. On waves on a string, speed is directly proportional to tension

  2. Velocity = square root T/mu

  3. As mass per length increases, velocity decreases

  4. Length of first harmonic of a rope with two free ends: wavelength / 2

  5. Length of first harmonic of a rope with one end fixed the other free: wavelength / 4
• When waves meet they pass through each other
• Wave characteristics


  • In a stationary wave, all particles except at nodes vibrate at the same frequency
  • In a progressive wave, all particles vibrate at the same frequency
  • In a progressive wave, amplitude is the same for all particles
  • In a stationary wave, phase difference equals to m x pi, where m is the number of nodes
  • In a progressive wave, phase difference equals to 2 x pi x d / wavelength (d = distance)
• Stationary waves transfer no energy to their surroundings
• If two waves reach the same point at the same time, add amplitudes and wavelengths
• Fundamental frequency = first harmonic
• Refraction is when a change of direction occurs when light hits a point
• Light rays bend


  • Towards normal in air to glass
  • Away from normal from glass to air