stationary waves

• a stationary wave is the superposition of two progressive waves with the same frequency and wavelength, moving in opposite directions.
• unlike progressive waves, no energy is transmitted by a stationary wave.
• you can demonstrate stationary waves by setting up a driving oscillator at one end of a stretched string with the other end fixed. the wave generated by the oscillator is reflected back and forth.

  for most frequencies, there resultant pattern is a jumble, however if the oscillator produces an exact number of waves in the time it takes for a wave to get to the end of back, then the original and reflected waves reinforce each other. these are called resonant frequencies, and you get a stationary wave where the pattern doesn't move, it just oscillates on the spot
• resonant frequencies are frequencies where a stationary wave is produced.

  at resonant frequencies, an exact number of half wavelengths fit onto the string.
• nodes are points where the amplitude of the vibration is zero.

  antinodes are points of maximum amplitude
• in stationary waves, each particle vibrates at right angles to the string
• at the first harmonic, the stationary wave is vibrating at the lowest possible resonant frequency. it has one antinode and two nodes
• this is the first harmonic. there is one antinode and two nodes

  
• this is the second harmonic. there are two antinodes and three nodes

  
• this is the third harmonic. there are three antinodes and four nodes

  
• you can demonstrate stationary waves with microwaves:

  • you can find the nodes and antinodes by moving the probe between the transmitter and the reflective metal plate

  
• you can demonstrate stationary waves in a tube of air:

  • stationary sound waves are produced in a glass tube
  • some powder is laid along the bottom of the tube, and it is shaken away from the antinodes but left undisturbed at the nodes

  
• investigating factors affecting resonant frequencies of a string:

  • set up a string fixed to a signal generator, connected to a pulley with masses attached to the end of the string
  • turn on the signal generator and vary the frequency until you find the first harmonic (which has two nodes and one antinode)
  • investigate how different factors affect this resonant frequency
• investigating factors affecting resonant frequencies of a string:

  • expected results:
  • the longer the string, the lower the resonant frequency as the half wavelength at the resonant frequency is longer
  • the heavier the string, the lower the resonant frequency as waves travel more slowly down the string
  • the looser the string, the lower the resonant frequency as waves travel more slowly down a loose string