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Stationary Waves (CIE AS Physics)

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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

Formation of a stationary wave

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

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 forced to vibrate due to an oscillator:

Standing wave experiment

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

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

Stationary microwaves

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

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 loud speaker at the open end of an air column with fine powder inside 
  • 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

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

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

Examiner Tip

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.

Formation of stationary waves

  • 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 wave 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 and antinodes, downloadable AS & A Level Physics revision notes

 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
  • Changing the frequency of the stationary wave produced will change the number of nodes and antinodes produced and consequently the wavelength

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Stationary waves are produced at varying frequencies

Worked example

A stretched string is used to demonstrate a stationary wave, as shown in the diagram.WE - Nodes and Antinodes question image(1), downloadable AS & A Level Physics revision notesWhich row in the table correctly describes the length of L and the name of X and Y?

  Length L Point X Point Y
A 5 wavelengths Node Antinode
B 1 half wavelengths Antinode Node
C 1 half wavelengths Node Antinode
D 5 wavelengths Antinode Node

Answer: C

Step 1: Determine the number of wavelengths in the length of the string

  • The string has 2 1 half wavelengths
    • This rules out A and D

Step 2: Determine points X and Y 

  • X is a point of 0 displacement - a node
  • Y is a point of maximum displacement - an antinode
    • Therefore, the correct row is C

Examiner Tip

The lengths of the strings will only be in terms of whole or ½ wavelengths. For example, a wavelength could be made up of 3 nodes and 2 antinodes or 2 nodes and 3 antinodes.

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Ashika

Author: Ashika

Expertise: Physics Project Lead

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.