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

Exam code: 7408

Katie M

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Katie M

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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

Constructive and destructive, downloadable AS & A Level Physics revision notes

Waves in superposition can undergo constructive or destructive interference

  • 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

Formation of stationary waves (1), downloadable AS & A Level Physics revision notes

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

  • 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)

Superposition of stationary waves, downloadable AS & A Level Physics revision notes

A graphical representation of how stationary waves are formed - the black line represents the resulting wave

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:

Stationary wave string, downloadable AS & A Level Physics revision notes

Stationary wave on a stretched string

  • 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

Stationary wave microwave, downloadable AS & A Level Physics revision notes

Using microwaves to demonstrate stationary waves

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

Air column stationary waves, downloadable AS & A Level Physics revision notes

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

Examiner Tips and Tricks

Always refer back to the experiment or scenario in an exam question e.g. the wave produced by a loudspeaker reflects at the end of a tube. This reflected wave, with the same frequency, overlaps the initial wave to create a stationary wave.

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Katie M

Author: Katie M

Expertise: Physics Content Creator

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.

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