Stationary Waves (Cambridge International AS Physics)

Spec point — 8.1.2

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

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 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

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 loudspeaker 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

Stationary waves can be seen in air columns using dry powder

• 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

Exam Hint 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 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

Stationary waves are produced at varying frequencies

Worked Example A stretched string is used to demonstrate a stationary wave, as shown in the diagram.

Which 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	2 $\frac{1}{2}$ wavelengths	Antinode	Node
C	2 $\frac{1}{2}$ 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 $\frac{1}{2}$ wavelengths

  • This rules out A and D

Step 2: Determine points X and Y

• X has zero amplitude – a node

• Y has maximum amplitude – an antinode

  • Therefore, the correct row is C

Exam Hint 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.