# 3.2.1 Stationary Waves

### 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
• Stationary waves store energy, unlike progressive waves which transfer energy

Formation of a stationary wave on a stretched spring fixed at one end

Comparing Progressive & Stationary Waves

### 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?

#### Exam Tip

Make sure you learn the definitions of node and antinode:

• Node = A point of minimum or no disturbance
• 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 3 nodes and 2 antinodes or 2 nodes and 3 antinodes.

### Author: Katie

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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