Stationary Waves

• Stationary waves are formed when 2 progressive waves with the same frequency travelling in opposite directions superpose.

  
  

  They do not transfer energy, they store it
• Stationary waves are formed when two waves travelling in opposite directions with the same frequency + amplitude, reflected of a fixed end, superpose creating nodes and antinodes
• Antinode: Point of maximum amplitude

  Node: Point of zero amplitude

  Between adjacent nodes all particles are in phase

  Particles on different sides of a node are in antiphase (180 degrees out of phase)
• Progressive Waves transfer energy in the direction of travel

  Stationary waves - no energy is transferred, it is stored

  Progressive waves the amplitude is constant

  Stationary waves the amplitude varies across nodes- 0 amplitude

  and antinodes - maximum amplitude
• Harmonics for closed at both ends:

  F0 = L = lander/2

  F1 = L = Lander

  F2 = L = 3*L/2

  F3 = L = 2 * Lander
• Harmonics closed at one end:

  1st = L = 1 /4 * Lander

  2nd = L = 3/4 * Lander

  3rd = L = 5/4 * Lander