Waves

• What is a progressive wave?

  A wave that transfers energy without transferring material and made from particles of a medium oscillating
• 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 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 in the wave cycle
• If points on a wave are in phase...

  They will have the same displacement and velocity and their phase difference will be a multiple of 360 degrees (or 2 pi radians)
• If two points are out of phase...

  They're an odd integer of half cycles apart (where one half cycle = 180 degrees or pi radians)
• Wave speed equation

  c = fλ
• Frequency equation

  f = 1/T
• Transverse waves

  The oscillation of particles is perpendicular to the direction of energy transfer
• Examples of transverse waves

  Electromagnetic waves, water waves
• Longitudinal waves

  Oscillation of waves is parallel to the direction of energy transfer.

  Made from compressions and rarefactions and cannot travel in a vacuum
• Examples of longitudinal waves

  Sound waves, pushing a slinky horizonatally
• Polarised waves can...

  Only travel in one plane (meaning 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)
• Example of polarisation

  Polarised sunglasses, TV and radio signals
• How do polarised sunglasses work?

  They reduce glare by blocking partially polarised light reflected from water or tarmac as they only allow oscillations in the plane of the filter making it easier to see.
• How is polarisation used in TV and radio signals?

  They are plane-polarised by the orientation of the rods on the transmitting aerial, so the receiving aerial must be aligned in the same plane of polarisation to receive the signal at full strength
• Superposition

  where 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
• A stationary wave is 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
• What happens when waves meet in phase?

  Constructive interference occurs so antinodes are formed which are regions of maximum amplitude.

  Destructive interference occurs where the waves meet out of phase so nodes are formed which are regions on no displacement
• How can a stationary wave be formed?

  Using a string fixed at one end, and fixed to a driving oscillator at the other.

  A wave travelling down the string from the oscillator will be reflected at the fixed end of the string, and travel back along the string causing superposition of the two waves, and because the waves have the same wavelength, frequency and amplitude, a stationary wave is formed.
• First harmonic 


  The lowest frequency at which a stationary wave forms.
• For the first harmonic, the distance between adjacent nodes is half the wavelength
• Equation for frequency

  Where L is the length of the vibrating string, T is the tension and μ is the mass per unit length.

  
• You can double the first harmonic frequency to find the second harmonic where there are 2 antinodes
• Examples of stationary waves

  Stationary microwaves, stationary sound waves
• Stationary microwaves

  formed by reflecting a microwave beam at a metal plate, to find the nodes and antinodes use a microwave probe.
• Stationary sound waves

  formed by placing a speaker at one end of a closed glass tube, lay powder across the bottom of the tube, it will be shaken at the antinodes and settle at the nodes
• Path difference

  Is the difference in distance travelled by two waves
• Coherence 


  Same frequency and constant phase difference
• Example of monochormatic light

  A laser
• Young's double slit

  Shine a light through 2 slits about the same size as the wavelength so the light diffracts. Each slit acts as a coherent point source so a pattern of light and dark fringes are formed.
• How are dark fringes formed?

  Where light meets completely out of phase and destructive interference occurs. Path difference is a whole and half number of wavelengths