3.1.6

# Stationary Waves

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## Stationary Waves

Stationary waves are important physical concepts. They can be created when a wave interferes with its reflection.

### Definition

• A stationary wave is formed when two progressive waves, each with the same frequency and wavelength and moving in opposite directions, interfere with one another.
• This creates a wave which doesn't transfer energy from one place to another.

### Nodes

• Nodes are points on a stationary wave that have zero amplitude.
• Having zero amplitude means that they are stationary.

### Antinodes

• Antinodes are points on a stationary wave with maximum amplitude.
• They oscillate from the furthest point upwards to the furthest point downwards.

## Resonance and Harmonics

Stationary waves can only have certain frequencies. These frequencies are called resonant frequencies. Each resonant frequency is called a harmonic.

### Resonance - first harmonic

• Stationary waves can only happen at resonant frequencies.
• Resonant frequencies happen when the distance between the two fixed ends is an integer multiple of half wavelengths, ½λ.
• The first resonant frequency is called the first harmonic.
• It happens when the distance between the two fixed ends is exactly ½λ.
• The first harmonic is shown in the diagram.
• It has two nodes and one antinode.
• The first harmonic is also known as the fundamental.

### Second harmonic

• The second resonant frequency is called the second harmonic.
• It happens when the distance between the two fixed ends is exactly λ.
• It contains two ½λ lengths.
• The second harmonic has a frequency twice as big as the first harmonic.
• It has three nodes and two antinodes.

### Third harmonic

• The third resonant frequency is called the third harmonic.
• It happens when the distance between the two fixed ends is exactly 1½λ.
• It contains three ½λ lengths.
• The third harmonic has a frequency three times as big as the first harmonic.
• It has four nodes and three antinodes.