Editing Node (physics) (section)

== Examples ==

=== 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 number of nodes in a specified length is directly proportional to the frequency of the wave.

Occasionally on a guitar, violin, or other stringed instrument, nodes are used to create [[harmonic]]s. 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 (instrument)|bridge]] and [[nut (instrument)|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 frequency|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.

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.

[[File:Bowing chladni plate.png|thumb|left|Sand highlights nodes on a Chladni plate.]]

===Waves in two or three dimensions===
[[File:HAtomOrbitals.png|thumb|Radial and angular nodes on hydrogen wavefunctions.]]

In two dimensional standing waves, nodes are curves (often straight lines or circles when displayed on simple geometries.) For example, sand collects along the nodes of a vibrating [[Ernst Chladni|Chladni plate]] to indicate regions where the plate is not moving.<ref>Comer, J. R., et al. [https://aapt.scitation.org/doi/pdf/10.1119/1.1758222 "Chladni plates revisited."] American journal of physics 72.10 (2004): 1345-1346.</ref>

In chemistry, [[quantum mechanics|quantum mechanical]] waves, or "[[atomic orbital|orbitals]]", are used to describe the wave-like properties of electrons. Many of these quantum waves have nodes and antinodes as well. The number and position of these nodes and antinodes give rise to many of the properties of an atom or [[covalent bond]]. Atomic orbitals are classified according to the number of radial and angular nodes. A radial node for the hydrogen atom is a sphere that occurs where the [[wavefunction]] for an atomic orbital is equal to zero, while the angular node is 
a flat plane.<ref>Supplemental modules (physical and Theoretical Chemistry). Chemistry LibreTexts. (2020, December 13). Retrieved September 13, 2022, from https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)</ref>

[[Molecular orbital]]s are classified according to bonding character. Molecular orbitals with an antinode between nuclei are very stable, and are known as "bonding orbitals" which strengthen the bond. In contrast, molecular orbitals with a node between nuclei will not be stable due to electrostatic repulsion and are known as "anti-bonding orbitals" which weaken the bond. Another such [[quantum mechanics|quantum mechanical]] concept is the [[particle in a box]] where the number of nodes of the wavefunction can help determine the quantum energy state&mdash;zero nodes corresponds to the ground state, one node corresponds to the 1st excited state, etc. In general,<ref>[[Albert Messiah]], 1966. ''Quantum Mechanics'' (Vol. I), English translation from French by G. M. Temmer. North Holland, John Wiley & Sons. Cf. chpt. IV, section III. [https://archive.org/details/QuantumMechanicsVolumeI   online]  Ch 3  §12</ref> ''If one arranges the eigenstates in the order of increasing energies, <math>\epsilon_1,\epsilon_2, \epsilon_3,...</math>, the eigenfunctions likewise fall in the order of increasing number of nodes; the ''n''th eigenfunction has ''n−1'' nodes, between each of which the following eigenfunctions have at least one node''.