Node (physics)

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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.

Contents 1 Explanation 2 Examples of longitudinal waves 2.1 Sound 2.2 Chemistry

[edit] Explanation

There are two types of wave propagation: longitudinal and transverse. An example of the former is the guitar string, which creates sound 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 the tips of a dipole antenna voltage antinodes and current nodes exist.

[edit] Examples of longitudinal waves

[edit] Sound

In a longitudinal wave (i.e. sound), the disturbance proceeds in the direction of wave propagation. Sound wave is alternations of the compression and the rarefaction of the molecules of the medium. During compression the molecules of the medium are forced together, resulting in the increased pressure or density, thus positive value. During rarefaction the molecules are forced apart, resulting in the decreased pressure, thus negative value. The zero value represents evenly spaced molecules.

As the frequency of a wave increases, there is an increase in the number of nodes. The number of nodes is directly proportional to the frequency of the wave.

On a guitar, violin, or other stringed instruments, 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 node is created and a harmonic is sounded. These harmonics release the quieter (but always present) overtone. If the finger is placed at the midpoint of the string, the first overtone is heard, which is an octave above the note which would be played, had the harmonic not been sounded. Splitting the string into thirds using the same method creates an octave and a perfect fifth (twelfth). Splitting the string into quarters creates a double octave. Splitting the string into fifths create a double-octave and a major third (17th). The octave, major third and perfect fifth are the three notes present in a major chord. Harmonic tones are sweet in character and blend well with other instruments.

[edit] 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.