3.3.1 Progressive and stationary waves

3.3.1 Progressive and stationary waves

1. Progressive waves

   • know amplitude, frequency, wavelength, speed
   • c = fλ = λ / T
     • f = 1/T
   • phase - the fraction of a cycle a vibrating particle has completed since the start of the cycle
     • phase difference - the fraction of a cycle between the vibrations between two particles vibration at the same frequency
       • 1 cycle = 360 degrees = 2π

2. Longitudinal and transverse waves

   • Longitude - waves with a direction of vibration parallel to the direction of propagation of the waves
   • Transverse - waves with a direction of vibration perpendicular to the direction of propagation of the waves
   • longitudinal examples
     • sound, primary seismic
   • transverse examples
     • em, secondary seismic
       • em - radio, micro, IF, visible light, UV, X-ray, gamma
         • all em waves travel at the same speed in a vacuum
   • Polarisation
     • transverse waves are plane polarised if the vibrations stay in one plane only
     • longitudinal waves cannot be polarised
     • if light from a candle passes through a polaroid filter, the transmitted ligh is polarised as the filter only allows through light which vibrates in a certain direction, according to the alignment of its molecules
       • if this light passes through a second polaroid at right angle to the first, no light will pass through the second
     • radio waves from a transmitter are polarised so aerial of a radio receiver needs to be aligned in the same plane as the radio waves to obtain the best reception

3. Principle of superposition of waves and formation of stationary waves

   • principle of superposition - when two waves meet, the total displacement at a point is equal to the sum of the individual displacement at that point
     • supercrest when two crests meet and reinforce
     • supertrough when two troughs meet and reinforce
     • zero amplitude when a crest and trough of the same amplitude meet
   • stationary waves on a rope
     • formed if two people send waves continuously along a rope from either end
       • combine at fixed points along the rope to form points of no displacement (nodes)
         • 180 degrees out of phase at the nodes
   • distance between adjacent nodes = λ/2
   • INTERFERENCE
     • interference patterns only produced when sources are coherent
     • constructive interference occurs when path difference = nλ
     • destructive interference occurs when path difference = (n+0.5)λ