Node (physics)

# Node (physics)

Discussion

Encyclopedia
A node is a point along a standing wave
Standing wave
In physics, a standing wave – also known as a stationary wave – is a wave that remains in a constant position.This phenomenon can occur because the medium is moving in the opposite direction to the wave, or it can arise in a stationary medium as a result of interference between two waves traveling...

where the wave has minimal amplitude
Amplitude
Amplitude is the magnitude of change in the oscillating variable with each oscillation within an oscillating system. For example, sound waves in air are oscillations in atmospheric pressure and their amplitudes are proportional to the change in pressure during one oscillation...

. For instance, in a vibrating guitar
Guitar
The guitar is a plucked string instrument, usually played with fingers or a pick. The guitar consists of a body with a rigid neck to which the strings, generally six in number, are attached. Guitars are traditionally constructed of various woods and strung with animal gut or, more recently, with...

string, the ends of the string are nodes. By changing the position of the end node through frets, the guitarist changes the effective length of the vibrating string
Vibrating string
A vibration in a string is a wave. Usually a vibrating string produces a sound whose frequency in most cases is constant. Therefore, since frequency characterizes the pitch, the sound produced is a constant note....

and thereby the note
Note
In music, the term note has two primary meanings:#A sign used in musical notation to represent the relative duration and pitch of a sound;#A pitched sound itself....

played. The opposite of a node is an anti-node, a point where the amplitude of the standing wave is a maximum. These occur midway between the nodes.

## Explanation

Standing wave
Standing wave
In physics, a standing wave – also known as a stationary wave – is a wave that remains in a constant position.This phenomenon can occur because the medium is moving in the opposite direction to the wave, or it can arise in a stationary medium as a result of interference between two waves traveling...

s result when two sinusoidal wave trains of the same frequency
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...

are moving in opposite directions in the same space and interfere with each other. They occur when waves are reflected at a boundary, such as sound waves reflected from a wall or electromagnetic waves reflected from the end of a transmission line
Transmission line
In communications and electronic engineering, a transmission line is a specialized cable designed to carry alternating current of radio frequency, that is, currents with a frequency high enough that its wave nature must be taken into account...

, and particularly when waves are confined in a resonator
Resonator
A resonator is a device or system that exhibits resonance or resonant behavior, that is, it naturally oscillates at some frequencies, called its resonant frequencies, with greater amplitude than at others. The oscillations in a resonator can be either electromagnetic or mechanical...

at resonance
Resonance
In physics, resonance is the tendency of a system to oscillate at a greater amplitude at some frequencies than at others. These are known as the system's resonant frequencies...

, bouncing back and forth between two boundaries, such as in an organ pipe
Organ pipe
An organ pipe is a sound-producing element of the pipe organ that resonates at a specific pitch when pressurized air is driven through it. Each pipe is tuned to a specific note of the musical scale...

or guitar string.

In a standing wave the nodes are a series of locations at equally spaced intervals where the wave amplitude
Amplitude
Amplitude is the magnitude of change in the oscillating variable with each oscillation within an oscillating system. For example, sound waves in air are oscillations in atmospheric pressure and their amplitudes are proportional to the change in pressure during one oscillation...

(motion) is zero (see animation above). At these points the two waves add with opposite phase
Phase (waves)
Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.-Formula:The phase of an oscillation or wave refers to a sinusoidal function such as the following:...

and cancel each other out. They occur at intervals of half a wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...

(λ/2). Midway between each pair of nodes are locations where the amplitude is maximum. These are called the antinodes. At these points the two waves add with the same phase and reinforce each other.

In cases where the two opposite wave trains are not the same amplitude, they do not cancel perfectly, so the amplitude of the standing wave at the nodes is not zero but merely a minimum. This occurs when the reflection at the boundary isn't perfect. This is indicated by a finite standing wave ratio
Standing wave ratio
In telecommunications, standing wave ratio is the ratio of the amplitude of a partial standing wave at an antinode to the amplitude at an adjacent node , in an electrical transmission line....

(SWR), the ratio of the amplitude of the wave at the antinode to the amplitude at the node.

In resonance
Resonance
In physics, resonance is the tendency of a system to oscillate at a greater amplitude at some frequencies than at others. These are known as the system's resonant frequencies...

of a two dimensional surface or membrane, such as a drumhead
A drumhead is a membrane stretched over one or both of the open ends of a drum. The drumhead is struck with sticks, mallets, or hands so that it vibrates and the sound resonates through the drum.-History:...

or vibrating metal plate, the nodes become nodal lines, lines on the surface where the surface is motionless, dividing the surface into separate regions vibrating with opposite phase. These can be made visible by sprinkling sand on the surface, and the intricate patterns of lines resulting are called Chladni figures.

In transmission line
Transmission line
In communications and electronic engineering, a transmission line is a specialized cable designed to carry alternating current of radio frequency, that is, currents with a frequency high enough that its wave nature must be taken into account...

s a voltage
Voltage
Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points...

node is erfect current
Electric current
Electric current is a flow of electric charge through a medium.This charge is typically carried by moving electrons in a conductor such as wire...

antinode, and a voltage antinode is a current node.

## Boundary conditions

Where the nodes occur in relation to the boundary reflecting the waves depends on the end conditions or boundary conditions. Although there are many types of end conditions, the ends of resonators are usually one of two types that cause total reflection:
• Fixed boundary: Examples of this type of boundary are the attachment point of a guitar
Guitar
The guitar is a plucked string instrument, usually played with fingers or a pick. The guitar consists of a body with a rigid neck to which the strings, generally six in number, are attached. Guitars are traditionally constructed of various woods and strung with animal gut or, more recently, with...

string, the closed end of an organ pipe
Organ pipe
An organ pipe is a sound-producing element of the pipe organ that resonates at a specific pitch when pressurized air is driven through it. Each pipe is tuned to a specific note of the musical scale...

or woodwind pipe, the periphery of a drumhead
A drumhead is a membrane stretched over one or both of the open ends of a drum. The drumhead is struck with sticks, mallets, or hands so that it vibrates and the sound resonates through the drum.-History:...

, a transmission line
Transmission line
In communications and electronic engineering, a transmission line is a specialized cable designed to carry alternating current of radio frequency, that is, currents with a frequency high enough that its wave nature must be taken into account...

with the end short circuit
Short circuit
A short circuit in an electrical circuit that allows a current to travel along an unintended path, often where essentially no electrical impedance is encountered....

ed, or the mirrors at the ends of a laser cavity. In this type, the amplitude of the wave is forced to zero at the boundary, so there is a node at the boundary, and the other nodes occur at multiples of half a wavelength from it:

0,  λ/2,  λ,  3λ/2,  2λ, ...

• Free boundary: Examples of this type are an open-ended organ or woodwind pipe, the ends of the vibrating resonator bars in a xylophone
Xylophone
The xylophone is a musical instrument in the percussion family that consists of wooden bars struck by mallets...

, glockenspiel
Glockenspiel
A glockenspiel is a percussion instrument composed of a set of tuned keys arranged in the fashion of the keyboard of a piano. In this way, it is similar to the xylophone; however, the xylophone's bars are made of wood, while the glockenspiel's are metal plates or tubes, and making it a metallophone...

or tuning fork
Tuning fork
A tuning fork is an acoustic resonator in the form of a two-pronged fork with the prongs formed from a U-shaped bar of elastic metal . It resonates at a specific constant pitch when set vibrating by striking it against a surface or with an object, and emits a pure musical tone after waiting a...

, the ends of an antenna
An antenna is an electrical device which converts electric currents into radio waves, and vice versa. It is usually used with a radio transmitter or radio receiver...

, or a transmission line with an open end. In this type the derivative (slope) of the wave's amplitude (in sound waves the pressure, in electromagnetic waves the current
Electric current
Electric current is a flow of electric charge through a medium.This charge is typically carried by moving electrons in a conductor such as wire...

) is forced to zero at the boundary. So there is an amplitude maximum (antinode) at the boundary, the first node occurs a quarter wavelength from the end, and the other nodes are at half wavelength intervals from there:

λ/4,  3λ/4,  5λ/4,  7λ/4, ...

### 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
Harmonic
A harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency, i.e. if the fundamental frequency is f, the harmonics have frequencies 2f, 3f, 4f, . . . etc. The harmonics have the property that they are all periodic at the fundamental...

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
Bridge (instrument)
A bridge is a device for supporting the strings on a stringed instrument and transmitting the vibration of those strings to some other structural component of the instrument in order to transfer the sound to the surrounding air.- Explanation :...

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
Overtone
An overtone is any frequency higher than the fundamental frequency of a sound. The fundamental and the overtones together are called partials. Harmonics are partials whose frequencies are whole number multiples of the fundamental These overlapping terms are variously used when discussing the...

is louder and the fundamental
Fundamental
Fundamental may refer to:* Foundation of reality* Fundamental frequency, as in music or phonetics, often referred to as simply a "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.

### Chemistry

In chemistry, quantum mechanical
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

waves, or "orbitals
Atomic orbital
An atomic orbital is a mathematical function that describes the wave-like behavior of either one electron or a pair of electrons in an atom. This function can be used to calculate the probability of finding any electron of an atom in any specific region around the atom's nucleus...

", 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 as likely form bonds between other noble gasses. Another such quantum mechanical
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

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.