(1) Progressive and stationary waves

• What is a progressive wave?

  A progressive wave transfers energy without transferring material
• What are the components of a progressive wave?

  Particles of a medium (or field) oscillating
• What is the amplitude of a wave?

  The maximum displacement from the equilibrium position
• What is the frequency of a wave?

  The number of complete oscillations passing through a point per second
• What is the wavelength of a wave?

  The length of one whole oscillation
• What is the speed of a wave?

  The distance travelled by the wave per unit time
• What is the phase of a wave?

  The position of a certain point on a wave cycle
• What is the phase difference between two points on a wave?

  How much a particle/wave lags behind another particle/wave
• What is the period of a wave?

  The time taken for one full oscillation
• When are two points on a wave in phase?

  When they are both at the same point of the wave cycle, have the same displacement and velocity, and their phase difference is a multiple of 360°
• When are two points on a wave completely out of phase?

  When they are an odd integer of half cycles apart
• What is the formula to calculate the speed of a wave?

  $c =$$f\lambda$
• What is the formula to calculate the frequency of a wave?

  $f =$$\frac{1}{T}$
• What are the characteristics of transverse waves?

  • Oscillation of particles (or fields) is at right angles to the direction of energy transfer
  • All electromagnetic (EM) waves are transverse and travel at 3 x 10^8 m/s in a vacuum
  • Can be demonstrated by shaking a slinky vertically or waves on a string attached to a signal generator
• What are the characteristics of longitudinal waves?

  • Oscillation of particles is parallel to the direction of energy transfer
  • Made up of compressions and rarefactions, cannot travel in a vacuum
  • Sound is an example, can be demonstrated by pushing a slinky horizontally
• What is a polarized wave?

  A wave that oscillates in only one plane
• Why can only transverse waves be polarized?

  Because polarization can only occur if a wave's oscillations are perpendicular to its direction of travel, as they are in transverse waves
• How do polaroid sunglasses work?

  They reduce glare by blocking partially polarized light reflected from water and tarmac, as they only allow oscillations in the plane of the filter
• How are TV and radio signals usually polarized?

  They are usually plane-polarized by the orientation of the rods on the transmitting aerial
• What is superposition of waves?

  • The displacements of two waves are combined as they pass each other
  • The resultant displacement is the vector sum of each wave's displacement
  • Can result in constructive interference (waves have displacement in the same direction) or destructive interference (one wave has positive displacement, the other has negative displacement)

  
• What is a stationary wave?

  • Formed from the superposition of two 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
  • Where the waves meet in phase, constructive interference occurs and antinodes (regions of maximum amplitude) are formed
  • Where the waves meet completely out of phase, destructive interference occurs and nodes (regions of no displacement) are formed

  
• What is the formula to calculate the frequency of the first harmonic of a stationary wave?

  $f =$$\frac{1}{2L}\sqrt{\frac{T}{\mu}}$
• How can you find the nodes and antinodes of a stationary wave?

  • For stationary microwaves, use a microwave probe
  • For stationary sound waves, lay powder across the bottom of a closed glass tube with a speaker at one end - the powder will be shaken at the antinodes and settle at the nodes
  • The distance between each node is half a wavelength, and the frequency of the signal generator to the speaker is known, so the speed of sound in air can be calculated using c = fλ
• How do the frequencies of the higher harmonics of a stationary wave relate to the first harmonic frequency?

  You can double the first harmonic frequency to find the second harmonic, triple it to find the third harmonic, and so on for the nth harmonic