Stationary Waves (AQA A Level Physics): Revision Note
Exam code: 7408
Stationary waves
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
Stationary waves store energy, unlike progressive waves which transfer energy
The following table compares the properties of progressive waves and stationary waves:
Progressive waves | Stationary waves |
|---|---|
All points have the same amplitude (in turn) | Each point has a different amplitude depending on the amount of superposition |
Points exactly a wavelength apart are in phase. The phase of points within one wavelength can be between 0 to 360° | Points between nodes are in phase. Points on either side of a node are out of phase |
Energy is transferred along the wave | Energy is stored, not transferred |
Does not have nodes or antinodes | Has nodes and antinodes |
The wave speed is the speed at which the wave moves through a medium | Each point on the wave oscillates at a different speed. The overall wave does not move |
Nodes & antinodes
A stationary wave is made up nodes and antinodes
Nodes are regions where there is no vibration
Antinodes are regions 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
The phase difference between two points on a stationary wave are either in phase or out of phase
Points between nodes are in phase with each other
Points that have an odd number of nodes between them are out of phase
Points that have an even number of nodes between them are in phase
The image below shows the nodes and antinodes on a snapshot of a stationary wave at a point in time
Where:
L is the length of the string
One wavelength λ is only a portion of the length of the string
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 | 2.5 wavelengths | Antinode | Node |
C | 2.5 wavelengths | Node | Antinode |
D | 5 wavelengths | Antinode | Node |
[1]
Answer:
Calculate how many wavelengths in the length of the string
This rules out rows A and D
Point X is a point of zero displacement, so it is a node
Point Y is a point of maximum displacement, so it is an antinode
Therefore, row C is the correct row [1 mark]
Examiner Tips and Tricks
Make sure you learn the definitions of node and antinode:
Node = A point of no vibration
Antinode = A point of maximum amplitude
In exam questions, the lengths of the strings will only be in whole or half wavelengths. For example, a wavelength could be made up of three nodes and two antinodes or two nodes and three antinodes.
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