Formation of Stationary Waves (AQA A Level Physics): Revision Note

Formation of stationary waves

The principle of superposition

• The principle of superposition states:

  When two or more waves with the same frequency arrive at a point, the resultant displacement is the sum of the displacements of each wave

• This principle describes how waves that meet at a point in space interact

• When two waves with the same frequency and amplitude arrive at a point, they superpose either:

  • In phase, causing constructive interference. The peaks and troughs line up on both waves and the resultant wave has double the amplitude

  • In anti-phase, causing destructive interference. The peaks on one wave line up with the troughs of the other. The resultant wave has no amplitude

• The principle of superposition applies to all types of waves i.e. transverse and longitudinal, progressive and stationary

The formation of stationary waves

• A stationary wave is formed when:

  Two waves travelling in opposite directions along the same line with the same frequency superpose

• The waves must have:

  • the same wavelength

  • a similar amplitude

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

• At the nodes:

  • The waves are in anti-phase meaning destructive interference occurs

  • This causes the two waves to cancel each other out

• At the antinodes:

  • The waves are in phase meaning constructive interference occurs

  • This causes the waves to add together

• Each point on the stationary wave has a different amplitude (unlike a progressive / travelling wave where each point has the same amplitude)

Examples of stationary waves

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:

• At specific frequencies, known as resonant frequencies, a whole number of half wavelengths will fit on the length of the string

• As the resonant frequencies of the oscillator are achieved, 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

Sound waves

• Sound waves can be produced as a result of the formation of stationary waves inside an air column

  • 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

• 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