4.9.7 Stationary Waves

• Stationary waves, or standing waves, are produced by the superposition of two waves of the same frequency and amplitude travelling in opposite directions
• This is usually achieved by a travelling wave and its reflection
  • The superposition produces a wave pattern where the peaks and troughs do not move

• Stationary waves store energy, unlike progressive waves which transfer energy

Formation of a stationary wave on a stretched spring fixed at one end

• Stationary waves can be represented by various mediums

Stretched String

• Vibrations caused by stationary waves on a stretched string produce sound
  • This is how stringed instruments, such as guitars or violins, work

• This can be demonstrated by a length of string under tension fixed at one end and vibrations made by an oscillator:

Stationary wave on a stretched string

• As the frequency of the oscillator changes, standing waves with different numbers of minima (nodes) and maxima (antinodes) form

Microwaves

• A microwave source is placed in line with a reflecting plate and a small detector between the two
• The reflector can be moved to and from the source to vary the stationary wave pattern formed
• By moving the detector, it can pick up the minima (nodes) and maxima (antinodes) of the stationary wave pattern

Using microwaves to demonstrate stationary waves

Air Columns

• The formation of stationary waves inside an air column can be produced by sound waves
  • This is how musical instruments, such as clarinets and organs, work

• This can be demonstrated by placing a fine powder inside the air column and a loudspeaker at the open end
• At certain frequencies, the powder forms evenly spaced heaps along the tube, showing where there is zero disturbance as a result of the nodes of the stationary wave

Stationary wave in an air column

• In order to produce a stationary wave, there must be a minima (node) at one end and a maxima (antinode) at the end with the loudspeaker

• A stationary wave is formed when two waves travelling in opposite directions along the same line overlap with each other
• The waves must have:
  • The same speed
  • The same frequency (or wavelength)
  • A similar amplitude

• As a result of superposition, a resultant wave is produced

Nodes and antinodes are a result of destructive and constructive interference respectively

• A stationary wave is made up of nodes and antinodes
• At the nodes:
  • The waves are in anti-phase meaning destructive interference occurs
  • This causes the two waves to cancel each other out and there is no vibration

• At the antinodes:
  • The waves are in phase meaning constructive interference occurs
  • This causes the waves to add together and the vibration is at maximum amplitude