# 5.9 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

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

• In this section, we will look at a few experiments that demonstrate stationary waves in everyday life

#### 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 an oscillator vibrating a length of string under tension fixed at one end:

Stationary wave on a stretched string

• 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

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 fine powder inside the air column and a loudspeaker at the open end
• 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 wave in an air column

• 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

#### Nodes and Antinodes

• A stationary wave is made up 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 along 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

• L is the length of the string
• 1 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

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.

Can't remember which is the node and which is the anti-node? Nodes occur at areas of NO Disturbance!

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