Stationary Waves (CIE A Level Physics)

• 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

Formation of a stationary wave

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

Stretched strings

• 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:

Standing wave experiment

Stationary wave on a stretched string kept taut by a mass and pulley system

• 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 waves in an air column

Stationary waves can be seen in air columns using dry power

• 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 made up of nodes and antinodes
  • Nodes are where there is no vibration
  • Antinodes are where the vibrations are at their maximum amplitude

• The nodes and antinodes do not move along the string. Nodes are fixed and antinodes only move in the vertical direction
• Between nodes, all points on the stationary are in phase
• The image below shows the nodes and antinodes on a snapshot of a stationary wave at a point in time

Nodes and antinodes on a stationary wave

 Nodes are points of zero amplitude, anti-nodes are points of maximum amplitude

• L is the length of the string
• 1 wavelength λ is only a portion of the length of the string