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.
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.
By shaking the spring faster still we could produce three loops four loops and so on.
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)
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)
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.
Practical examples of standing waves in wires
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.
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).