# Node (physics)

File:Standing wave.gif
A standing wave. The red dots are the wave nodes

A node is a point along a standing wave where the wave has minimal amplitude. This has implications in several fields. For instance, in a guitar string, the ends of the string are nodes. By changing the position of one of these nodes through frets, the guitarist changes the effective length of the vibrating string and thereby the note played. The opposite of a node is an anti-node, which is the farthest point from the node on a wave.

## Explanation

There are two types of wave propagation: longitudinal and transverse. In a longitudinal wave, the wave displacement occurs in the direction of wave propagation. In a transverse wave, the wave displacement occurs transverse (at right-angles, or orthogonal) to the direction of wave propagation.

An example of a transverse wave is a vibrating guitar string. However, sound waves are transverse pressure waves. You can easily see the displacement nodes, because they have minimal amplitude. Light and other electromagnetic waves are examples of transverse waves. It is possible in transmission lines which have high standing wave ratios to observe voltage and current nodes and antinodes. A voltage node is a current antinode, and a current node is a voltage antinode. For example at each end of a dipole antenna, there is a voltage antinode and a current node.

## Examples of longitudinal waves

### Sound

A sound wave consists of alternating cycles of compression and expansion of the wave medium. During compression the molecules of the medium are forced together, resulting in the increased pressure and density. During expansion the molecules are forced apart, resulting in the decreased pressure and density.

The density of nodes is directly proportional to the frequency of the wave.

Occasionally on a guitar, violin, or other stringed instrument, artificial nodes are used to create harmonics. When the finger is placed on top of the string at a certain point, but does not push the string all the way down to the fretboard, a third node is created (in addition to the bridge and nut) and a harmonic is sounded. During normal play when the frets are used, the harmonics are always present, although they are quieter. With the artificial node method, the overtone is louder and the fundamental tone is quieter. If the finger is placed at the midpoint of the string, the first overtone is heard, which is an octave above the fundamental note which would be played, had the harmonic not been sounded. When two additional nodes divide the string into thirds, this creates an octave and a perfect fifth (twelfth). When three additional nodes divide the string into quarters, this creates a double octave. When four additional nodes divide the string into fifths, this creates a double-octave and a major third (17th). The octave, major third and perfect fifth are the three notes present in a major chord.

When two or more instruments are played in keys that are harmonious, then harmonic tones may be considered to "blend" well and to be sweet in character. However when played in dissonant keys, harmonics may also carry rich dissonance. The musical quality is more a reflection of music theory, than of harmonics per se.

The characteristic sound that allows the listener to identify a particular instrument is largely due to the relative magnitude of the harmonics created by the instrument.

### Chemistry

In chemistry, quantum mechanical waves, or "orbitals", are used to describe the wave-like properties of electrons. Many of these quantum waves have nodes as well. The number and position of these nodes give rise to many of the properties of an atom or bond. For example, bonding orbitals with small nodes solely around nuclei are very stable, and are known as "bonds". In contrast, bonding orbitals with large nodes between nuclei will not be stable due to electrostatic repulsion and are known as "anti-bonding orbitals" because they will be so unstable as to cause a bond to break. It is due to this that the noble gases will not form bonds between other noble spaces. Another such quantum mechanical concept is the particle in a box where the number of nodes of the wavefunction can help determine the quantum energy state—zero nodes corresponds to the ground state, one node corresponds to the 1st excited state, etc.