stationary and progressive waves

stationary and progressive waves

1. formation

   • when two progressive waves pass through each other
     • achieved by fixing both ends and making the middle part vibrate, so progressive waves travel
   • stationary waves that vibrate freely don't transfer energy

2. node

   • point of no displacement
   • distance bewteen adjacent nodes = 1/2λ

3. antinodes

   • maximum amplitude midway between the nodes

4. explanation of stationary waves

   • waves in phase
     • they reinforce each other to produce a large wave
   • quarter of cycle later
     • the two waves has moved one quarter of a wavelength in opposite directions
       • waves in antiphase so they cancel out each other
   • further quarter cycle
     • waves back in phase
       • resultant is a large wave but reversed

5. stationary wave pattern

   • the amplitude
     • varies with position from zero at a node to max amplitude at an antinode
   • phase difference
     • zero if two particles are between adjacent nodes
     • 180° if two particles are separated by an odd number of nodes

6. examples

   • sound in a pipe
     • if pipe closed at one end
       • the antinode is at the open end
       • node at the close end
   • using microwaves

Images and files in the map