# 4.9.9 Nodes & Antinodes

### 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

#### 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.

### Calculating Wavelength from Nodes & Antinodes

• The wavelength λ of a stationary wave can be determined by the separation between adjacent nodes (or antinodes)

The separation between adjacent nodes or antinodes is equal to λ / 2

• Adjacent means two nodes or antinodes that are next to each other

#### Worked Example

The stationary wave below has a length L of 15 cm.

Calculate the wavelength λ of the wave.

Step 1: Calculate the distance between two nodes

Distance between two nodes = 15 cm ÷ 3 = 5 cm

Step 2: Calculate λ

Distance between two nodes = λ / 2 = 5 cm

λ = 2 × 5cm = 10 cm

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