What are standing waves in a wire

A standing wave in a wire is a fixed pattern of vibration - hence the term “standing wave”. By shaking a rope or a long spring we can make it form a loop, like this, oscillating up and down.

The Fundamental wave, the most simple wave that can be produced in a wire
Fundamental wave

By doubling the frequency of vibration we can produce a constant pattern of two loops. A standing wave with half the wavelength and double the frequency of the fundamental wave.

Double the frequency and half the wavelength of the fundamental
Double the frequency of the fundamental

By shaking the spring faster still we could produce three loops four loops and so on.

Treble the frequency and a third the wavelength of the fundamental
Treble the frequency of the fundamental

This pattern is caused by the wave traveling along the wire, reflecting from the ends of the string and interfering with itself on the way back. The red wave moving to the right and the purple wave moving to the left are meeting crest to trough. The resulting destructive interference produces no wave. (In black)

Destructive interference at the nodes of a standing wave
Destructive interference

The red wave moving to the right and the purple wave moving to the left are meeting crest to crest and trough to trough. The resulting constructive interference produces a large wave. (In black)

Constructive interference at the antinodes of the standing wave
Constructive interference

Nodes, antinodes and wavelength

The parts of the string/wire/spring that oscillates most is called the “antinode”, the parts that are still are called the “nodes”. One wavelength is the total distance between 3 nodes, that is across two loops, as shown below. The most simple vibration, a single loop is called the fundamental note. The wavelength of this note is twice the length of the string.

Comparing the wavelengths of standing waves
The wavelengths of standing waves

Practical examples of standing waves in wires

Guitar strings showing varying width and materials
Guitar strings

Musical instruments use standing waves to create the notes. The length of the string, the thickness and the tension all affect the note produced.

The more massive the string (longer and thicker) the more slowly it vibrates. Large masses are harder to accelerate. If the tension is low, then the forces are small and again it vibrates more slowly because small forces produce less acceleration.

School experiments with standing waves are commonly performed using a sonometer on which you can change the tension and length of the vibrating wire. This is pictured below. It consists of a moveable “bridge to vary the length of the wire and a weight or twisting post to apply (and change) the tension in the wire. Part of the wire, between the triangular bridges can be plucked to sound the note.laboratory sketch of a sonometer

A standard school sonometer
A sonometer

Standing waves can sometimes be dangerously created in large structures, such a buildings and bridges during storms or an earthquake. The bed of the bridge is quite clearly not a wire but this long thin length acts in the same way. This may be due to resonance and can be reduced by damping. (See further notes).

A standing wave in a bridge caused by high winds. The bridge acts like a wire.
A standing wave in a bridge

There are two other pages on standing / stationary waves each with video lessons: