In
physicsPhysics is a natural science; it is the study of matter and its motion through spacetime and all that derives from these, such as energy and force...
,
resonance is the tendency of a system to oscillate at larger
amplitudeAmplitude is the magnitude of change in the oscillating variable, with each oscillation, within an oscillating system. For instance, sound waves are oscillations in atmospheric pressure and their amplitudes are proportional to the change in pressure during one oscillation...
at some
frequenciesFrequency 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....
than at others. These are known as the system's
resonant frequencies (or
resonance frequencies). At these frequencies, even small
periodicIn mathematics, a periodic function is a function that repeats its values in regular intervals or periods. The most important examples are the trigonometric functions, which repeat over intervals of length 2π...
driving forces can produce large amplitude vibrations, because the system stores vibrational energy. When
dampingIn physics, damping is any effect that tends to reduce the amplitude of oscillations in an oscillatory system, particularly the harmonic oscillator.In mechanics, friction is one such damping effect...
is small, the resonant frequency is approximately equal to the natural frequency of the system, which is the frequency of free vibrations. Resonance phenomena occur with all types of vibrations or waves: there is
mechanical resonanceMechanical resonance is the tendency of a mechanical system to absorb more energy when the frequency of its oscillations matches the system's natural frequency of vibration than it does at other frequencies...
,
acoustic resonanceAcoustic resonance is the tendency of an acoustic system to absorb more energy when it is forced or driven at a frequency that matches one of its own natural frequencies of vibration than it does at other frequencies...
,
electromagneticElectromagnetic radiation is a ubiquitous phenomenon that takes the form of self-propagating waves in a vacuum or in matter. It consists of electric and magnetic field components which oscillate in phase perpendicular to each other and perpendicular to the direction of energy propagation...
resonance,
nuclear magnetic resonanceNuclear magnetic resonance is a property that magnetic nuclei have in a magnetic field and applied electromagnetic pulse, which cause the nuclei to absorb energy from the EM pulse and radiate this energy back out...
(NMR),
electron spin resonanceElectron paramagnetic resonance or electron spin resonance spectroscopyis a technique for studying chemical species that have one or more unpaired electrons, such as organic and inorganic free radicals or inorganic complexes possessing a transition metal ion...
(ESR) and resonance of quantum wave functions. Resonant systems can be used to generate vibrations of a specific frequency (e.g. musical instruments), or pick out specific frequencies from a complex vibration containing many frequencies.
Resonance was discovered by
Galileo GalileiGalileo Galilei was an Italian physicist, mathematician, astronomer, and philosopher who played a major role in the Scientific Revolution. His achievements include improvements to the telescope and consequent astronomical observations, and support for Copernicanism...
with his investigations of
pendulumA pendulum is a weight suspended from a pivot so it can swing freely.When a pendulum is displaced from its resting equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position. When released, the restoring force will cause it...
s and
musical stringsA string is the vibrating element that is the source of vibration in string instruments, such as the guitar, harp, piano, and members of the violin family. They are lengths of a flexible material kept under tension so that they may freely vibrate...
beginning in 1602.
Examples
One familiar example is a playground
swingA swing is a hanging seat, usually found in a playground for children, a circus for acrobats, or on a porch for relaxing. The seat of a swing can be attached to a chain or a rope...
, which acts as a
pendulumA pendulum is a weight suspended from a pivot so it can swing freely.When a pendulum is displaced from its resting equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position. When released, the restoring force will cause it...
. Pushing a person in a swing in time with the natural interval of the swing (its resonance frequency) will make the swing go higher and higher (maximum amplitude), while attempts to push the swing at a faster or slower tempo will result in smaller arcs. This is because the energy the swing absorbs is maximized when the pushes are 'in
phaseThe phase of an oscillation or wave is the fraction of a complete cycle corresponding to an offset in the displacement from a specified reference point at time t = 0. Phase is a frequency domain or Fourier transform domain concept, and as such, can be readily understood in terms of simple harmonic...
' with the swing's oscillations, while some of the swing's energy is actually extracted by the opposing force of the pushes when they are not.
Resonance occurs widely in nature, and is exploited in many man-made devices. It is the mechanism by which virtually all sinusoidal
waveA wave is a disturbance that propagates through space and time, usually with transference of energy. A mechanical wave is a wave that propagates or travels through a medium due to the restoring forces it produces upon deformation. There also exist waves capable of traveling through a vacuum,...
s and vibrations are generated. Many sounds we hear, such as when hard objects of metal, glass, or wood are struck, are caused by brief resonant vibrations in the object. Light and other short wavelength
electromagnetic radiationElectromagnetic radiation is a ubiquitous phenomenon that takes the form of self-propagating waves in a vacuum or in matter. It consists of electric and magnetic field components which oscillate in phase perpendicular to each other and perpendicular to the direction of energy propagation...
is produced by resonance on an atomic scale, such as electrons in atoms. Other examples are:
MechanicalMechanical resonance is the tendency of a mechanical system to absorb more energy when the frequency of its oscillations matches the system's natural frequency of vibration than it does at other frequencies...
and
acoustic resonanceAcoustic resonance is the tendency of an acoustic system to absorb more energy when it is forced or driven at a frequency that matches one of its own natural frequencies of vibration than it does at other frequencies...
- the timekeeping mechanisms of all modern clocks and watches: the balance wheel
The balance wheel is the timekeeping device used in mechanical watches and some clocks, analogous to the pendulum in a pendulum clock. It is a weighted wheel that rotates back and forth, being returned toward its center position by a spiral spring, the balance spring or hairspring...
in a mechanical watchA watch is a timepiece that is made to be worn on a person. It is usually a wristwatch, worn on the wrist with a strap or bracelet. In addition to the time, modern watches often display the day, date, month and year, and electronic watches may have many other functions.Most inexpensive and...
and the quartz crystal in a quartz watch
- the tidal resonance
In oceanography, a tidal resonance occurs when the tide excites one of the resonant modes of the ocean. The effect is most striking when a continental shelf is about a quarter wavelength wide...
of the Bay of FundyThe Bay of Fundy is a bay on the Atlantic coast of North America, on the northeast end of the Gulf of Maine between the Canadian provinces of New Brunswick and Nova Scotia, with a small portion touching the U.S. state of Maine...
- acoustic resonance
Acoustic resonance is the tendency of an acoustic system to absorb more energy when it is forced or driven at a frequency that matches one of its own natural frequencies of vibration than it does at other frequencies...
s of musical instruments and human vocal cords
- the resonance of the basilar membrane
The basilar membrane within the cochlea of the inner ear is a stiff structural element that separates two liquid-filled tubes that run along the coil of the cochlea, the scala media and the scala tympani .-Function:...
in the cochleaThe cochlea is the auditory portion of the inner ear. Its core component is the Organ of Corti, the sensory organ of hearing, which is distributed along the partition separating fluid chambers in the coiled tapered tube of the cochlea....
of the ear, which enables people to distinguish different frequencies or tones in the sounds they hear.
- the shattering of a crystal wineglass when exposed to a musical tone of the right pitch (its resonance frequency).
Electrical resonanceElectrical resonance occurs in an electric circuit at a particular resonance frequency when the impedance between the input and output of the circuit is at a minimum...
- electrical resonance
Electrical resonance occurs in an electric circuit at a particular resonance frequency when the impedance between the input and output of the circuit is at a minimum...
of tuned circuits in radioRadio is the transmission of signals by modulation of electromagnetic waves with frequencies below those of visible light. Electromagnetic radiation travels by means of oscillating electromagnetic fields that pass through the air and the vacuum of space...
s and TVs that allow individual stations to be picked up
Optical resonanceAn optical cavity or optical resonator is an arrangement of mirrors that forms a standing wave cavity resonator for light waves. Optical cavities are a major component of lasers, surrounding the gain medium and providing feedback of the laser light. They are also used in optical parametric...
- creation of coherent light by optical resonance in a laser
A laser is a device that emits light through a process called stimulated emission. Laser light is usually spatially coherent, which means that the light either is emitted in a narrow, low-divergence beam, or can be converted into one with the help of optical components such as lenses...
cavityAn optical cavity or optical resonator is an arrangement of mirrors that forms a standing wave cavity resonator for light waves. Optical cavities are a major component of lasers, surrounding the gain medium and providing feedback of the laser light. They are also used in optical parametric...
Orbital resonanceIn celestial mechanics, an orbital resonance occurs when two orbiting bodies exert a regular, periodic gravitational influence on each other, usually due to their orbital periods being related by a ratio of two small integers. Orbital resonances greatly enhance the mutual gravitational influence of...
in astronomyAstronomy is the scientific study of celestial objects and phenomena that originate outside the Earth's atmosphere...
- orbital resonance
In celestial mechanics, an orbital resonance occurs when two orbiting bodies exert a regular, periodic gravitational influence on each other, usually due to their orbital periods being related by a ratio of two small integers. Orbital resonances greatly enhance the mutual gravitational influence of...
as exemplified by some moonsA natural satellite or moon is a celestial body that orbits a planet or smaller body, which is called the primary. Technically, the term natural satellite could refer to a planet orbiting a star, or a dwarf galaxy orbiting a major galaxy, but it is normally synonymous with moon and used to identify...
of the solar systemThe Solar System consists of the Sun and those celestial objects bound to it by gravity, all of which formed from the collapse of a giant molecular cloud approximately 4.6 billion years ago...
's gas giantsGas Giants were a pop rock band from Tempe, Arizona, formed as a successor project to the Gin Blossoms. The group was known as The Pharaohs when they formed in 1997, but changed their name after their label, A&M Records, merged with Universal Records and the band changed hands, re-signing with...
Atomic, particle, and molecular resonance
- material resonances in atomic scale are the basis of several spectroscopic
Spectroscopy was originally the study of the interaction between radiation and matter as a function of wavelength . In fact, historically, spectroscopy referred to the use of visible light dispersed according to its wavelength, e.g. by a prism. Later the concept was expanded greatly to comprise...
techniques that are used in condensed matter physicsCondensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter. In particular, it is concerned with the "condensed" phases that appear whenever the number of constituents in a system is extremely large and the interactions between the...
.
- Nuclear Magnetic Resonance
Nuclear magnetic resonance is a property that magnetic nuclei have in a magnetic field and applied electromagnetic pulse, which cause the nuclei to absorb energy from the EM pulse and radiate this energy back out...
- Mössbauer effect
The Mössbauer effect is a physical phenomenon discovered by the German physicist Rudolf Mößbauer in 1957, and refers to the resonant and recoil-free emission and absorption of gamma ray photons by atoms bound in a solid form...
- Electron Spin Resonance.
Theory
The exact response of a resonance, especially for frequencies far from the resonant frequency, depends on the details of the physical system, and is usually not exactly symmetric about the resonant frequency, as illustrated for the simple harmonic oscillator above.
For a lightly
dampedIn physics, damping is any effect that tends to reduce the amplitude of oscillations in an oscillatory system, particularly the harmonic oscillator.In mechanics, friction is one such damping effect...
linear oscillator with a resonant frequency Ω, the
intensity of oscillations
I when the system is driven with a driving frequency ω is typically approximated by a formula that is symmetric about the resonant frequency:
The intensity is defined as the square of the amplitude of the oscillations. This is a Lorentzian function, and this response is found in many physical situations involving resonant systems. Γ is a parameter dependent on the
dampingIn classical mechanics, a harmonic oscillator is a system which, when displaced from its equilibrium position, experiences a restoring force, F, proportional to the displacement, x according to Hooke's law:where k is a positive constant....
of the oscillator, and is known as the
linewidth of the resonance. Heavily damped oscillators tend to have broad linewidths, and respond to a wider range of driving frequencies around the resonant frequency. The linewidth is
inversely proportionalIn mathematics, two quantities are said to be proportional if they vary in such a way that one of the quantities is a constant multiple of the other, or equivalently if they have a constant ratio.Proportion also refers to the equality of two ratios....
to the
Q factorIn physics and engineering the quality factor or Q factor is a dimensionless parameter that describes how under-damped an oscillator or resonator is, or equivalently, characterizes a resonator's bandwidth relative to its center frequency....
, which is a measure of the sharpness of the resonance.
In
electrical engineeringElectrical engineering, sometimes referred to as electrical and electronic engineering, is a field of engineering that deals with the study and application of electricity, electronics and electromagnetism. The field first became an identifiable occupation in the late nineteenth century after...
, this approximate symmetric response is known as the
universal resonance curve, a concept introduced by Frederick E. Terman in 1935 to simplify the approximate analysis of radio circuits with a range of center frequencies and Q values.
Resonators
A physical system can have as many resonance frequencies as it has
degrees of freedomIn mechanics, degrees of freedom are the set of independent displacements and/or rotations that specify completely the displaced or deformed position and orientation of the body or system...
; each degree of freedom can vibrate as a
harmonic oscillatorIn classical mechanics, a harmonic oscillator is a system which, when displaced from its equilibrium position, experiences a restoring force, F, proportional to the displacement, x according to Hooke's law:where k is a positive constant....
. Systems with one degree of freedom, such as a mass on a spring,
pendulumA pendulum is a weight suspended from a pivot so it can swing freely.When a pendulum is displaced from its resting equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position. When released, the restoring force will cause it...
s,
balance wheelThe balance wheel is the timekeeping device used in mechanical watches and some clocks, analogous to the pendulum in a pendulum clock. It is a weighted wheel that rotates back and forth, being returned toward its center position by a spiral spring, the balance spring or hairspring...
s, and
LC tuned circuitsAn RLC circuit is an electrical circuit consisting of a resistor , an inductor , and a capacitor , connected in series or in parallel. This configuration forms a harmonic oscillator....
have one resonance frequency. Systems with two degrees of freedom, such as
coupled pendulumsIn horology, a double pendulum is a system of two simple pendulums on a common mounting which move in anti-phase.In mathematics, in the area of dynamical systems, a double pendulum is a pendulum with another pendulum attached to its end, and is a simple physical system that exhibits rich dynamic...
and
resonant transformersA transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductors—the transformer's coils. A varying current in the first or primary winding creates a varying magnetic flux in the transformer's core, and thus a varying magnetic field...
can have two resonance frequencies. As the number of coupled harmonic oscillators grows, the time it takes to transfer energy from one to the next becomes significant. The vibrations in them begin to travel through the coupled harmonic oscillators in waves, from one oscillator to the next.
Extended objects that experience resonance due to vibrations inside them are called resonators, such as
organ pipeAn 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...
s,
vibrating stringA 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....
s, quartz crystals,
microwaveMicrowaves are electromagnetic waves with wavelengths ranging from as long as one meter to as short as one millimeter, or equivalently, with frequencies between 300MHz and 300 GHz. This is an extremely broad definition including both UHF and EHF , and various sources use different boundaries...
cavities, and
laserA laser is a device that emits light through a process called stimulated emission. Laser light is usually spatially coherent, which means that the light either is emitted in a narrow, low-divergence beam, or can be converted into one with the help of optical components such as lenses...
rods. Since these can be viewed as being made of millions of coupled moving parts (such as atoms), they can have millions of resonance frequencies. The vibrations inside them travel as waves, at an approximately constant velocity, bouncing back and forth between the sides of the resonator. If the distance between the sides is , the length of a round trip is . In order to cause resonance, the phase of a sinusoidal wave after a round trip has to be equal to the initial phase, so the waves will reinforce. So the condition for resonance in a resonator is that the round trip distance, , be equal to an integral number of wavelengths of the wave:
If the velocity of a wave is , the frequency is so the resonance frequencies are:
So the resonance frequencies of resonators, called normal modes, are equally spaced multiples of a lowest frequency called the
fundamental frequencyThe fundamental tone, often referred to simply as the fundamental and abbreviated f
0 or F
0, is the lowest frequency in a harmonic series....
. The multiples are often called
overtoneAn overtone is a natural resonance of a system. Systems described by overtones are often sound systems, for example, blown pipes or plucked strings.If such a system is excited, a number of tones may be produced along with the fundamental tone...
s. There may be several such series of resonance frequencies, corresponding to different modes of vibration.
Mechanical and acoustic resonance
Mechanical resonance is the tendency of a
mechanical systemMechanics is the branch of physics concerned with the behaviour of physical bodies when subjected to forces or displacements, and the subsequent effect of the bodies on their environment....
to absorb more energy when the
frequencyFrequency 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....
of its oscillations matches the system's natural frequency of
vibrationVibration refers to mechanical oscillations about an equilibrium point. The oscillations may be periodic such as the motion of a pendulum or random such as the movement of a tire on a gravel road.Vibration is occasionally "desirable"...
than it does at other frequencies. It may cause violent swaying motions and even catastrophic failure in improperly constructed structures including bridges, buildings, and airplanes.
EngineerEngineers are concerned with developing economical and safe solutions to practical problems, by applying mathematics and scientific knowledge while considering technical constraints. The term is derived from the Latin root "ingenium," meaning "cleverness"...
s when designing objects must ensure that the mechanical resonant frequencies of the component parts do not match driving vibrational frequencies of the motors or other oscillating parts a phenomenon known as resonance disaster.
Avoiding resonance disasters is a major concern in every building, tower and bridge
constructionIn the fields of architecture and civil engineering, construction is a process that consists of the building or assembling of infrastructure. Far from being a single activity, large scale construction is a feat of multitasking...
project. As a countermeasure, shock mounts can be installed to absorb resonant frequencies and thus dissipate the absorbed energy. The
Taipei 101Taipei 101 , also known as the Taipei Financial Center, is a landmark skyscraper located in Xinyi District, Taipei, Taiwan. The building, designed by C.Y...
building relies on a 730-ton
pendulumA pendulum is a weight suspended from a pivot so it can swing freely.When a pendulum is displaced from its resting equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position. When released, the restoring force will cause it...
— a
tuned mass damperA tuned mass damper, also known as an active mass damper or harmonic absorber, is a device mounted in structures to prevent discomfort, damage, or outright structural failure caused by vibration...
— to cancel resonance. Furthermore, the structure is designed to resonate at a frequency which does not typically occur. Buildings in seismic zones are often constructed to take into account the oscillating frequencies of expected ground motion. In addition,
EngineerEngineers are concerned with developing economical and safe solutions to practical problems, by applying mathematics and scientific knowledge while considering technical constraints. The term is derived from the Latin root "ingenium," meaning "cleverness"...
s designing objects having engines must ensure that the mechanical resonant frequencies of the component parts do not match driving vibrational frequencies of the motors or other strongly oscillating parts.
Many
clockA clock is an instrument used to indicate, measure, keep, and co-ordinate time. The word clock is derived ultimately from the Celtic words clagan and clocca meaning "bell"...
s keep time by mechanical resonance in a
balance wheelThe balance wheel is the timekeeping device used in mechanical watches and some clocks, analogous to the pendulum in a pendulum clock. It is a weighted wheel that rotates back and forth, being returned toward its center position by a spiral spring, the balance spring or hairspring...
,
pendulumA pendulum is a weight suspended from a pivot so it can swing freely.When a pendulum is displaced from its resting equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position. When released, the restoring force will cause it...
, or
quartz crystalA quartz clock is a clock that uses an electronic oscillator that is regulated by a quartz crystal to keep time. This crystal oscillator creates a signal with very precise frequency, so that quartz clocks are at least an order of magnitude more accurate than good mechanical clocks...
Acoustic resonanceAcoustic resonance is the tendency of an acoustic system to absorb more energy when it is forced or driven at a frequency that matches one of its own natural frequencies of vibration than it does at other frequencies...
is a branch of
mechanical resonanceMechanical resonance is the tendency of a mechanical system to absorb more energy when the frequency of its oscillations matches the system's natural frequency of vibration than it does at other frequencies...
that is concerned the mechanical vibrations in the frequency range of human hearing, in other words
soundSound is a travelling wave which is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard, or the sensation stimulated in organs of hearing by such vibrations.- Perception of sound...
. For humans, hearing is normally limited to frequencies between about 12
HzThe hertz is a unit of frequency. It is defined as the number of complete cycles per second. It is the basic unit of frequency in the International System of Units , and is used worldwide in both general-purpose and scientific contexts...
and 20,000 Hz (20 kHz),
Acoustic resonance is an important consideration for instrument builders, as most acoustic
instrumentsA musical instrument is an object constructed or used for the purpose of making the sounds of music. In principle, anything that produces sound can serve as a musical instrument. The history of musical instruments dates back to the beginnings of human culture...
use
resonatorA resonator is a device or system that exhibits resonance or resonant behavior, that is, it naturally oscillates at some frequencies, called its resonance frequencies, with greater amplitude than at others. The oscillations in a resonator can be either electromagnetic or mechanical...
s, such as the strings and body of a
violinThe violin is a bowed string instrument with four strings usually tuned in perfect fifths. It is the smallest and highest-pitched member of the violin family of string instruments, which also includes the viola and cello....
, the length of tube in a
fluteThe flute is a musical instrument of the woodwind group. Unlike woodwind instruments with reeds, a flute is an aerophone or reedless wind instrument that produces its sound from the flow of air across an opening...
, and the shape of a drum membrane. Acoustic resonance is also important for hearing. For example, resonance of a stiff structural element, called the
basilar membraneThe basilar membrane within the cochlea of the inner ear is a stiff structural element that separates two liquid-filled tubes that run along the coil of the cochlea, the scala media and the scala tympani .-Function:...
within the
cochleaThe cochlea is the auditory portion of the inner ear. Its core component is the Organ of Corti, the sensory organ of hearing, which is distributed along the partition separating fluid chambers in the coiled tapered tube of the cochlea....
of the
inner earThe inner ear is the bony labyrinth, a system of passages comprising two main functional parts:* The cochlea is the hearing part of the inner ear.* The semicircular canals , the utricle and the saccule are the balance part of the inner ear...
allows hairs on the membrane to detect sound. (For mammals the membrane by having different resonance on either end so that high frequencies are concentrated on one end and low frequencies on the other.)
Like mechanical resonance, acoustic resonance can result in catastrophic failure of the vibrator. The classic example of this is breaking a wine glass with sound at the precise resonant frequency of the glass; although this is difficult in practice.
Electrical resonance
Electrical resonance occurs in an
electric circuitAn electrical network is an interconnection of electrical elements such as resistors, inductors, capacitors, transmission lines, voltage sources, current sources, and switches....
at a particular
resonance frequencyIn physics, resonance is the tendency of a system to oscillate at larger amplitude at some frequencies than at others. These are known as the system's resonant frequencies . At these frequencies, even small periodic driving forces can produce large amplitude vibrations, because the system...
when the
impedanceElectrical impedance, or simply impedance, describes a measure of opposition to a sinusoidal alternating current . Electrical impedance extends the concept of resistance to AC circuits, describing not only the relative amplitudes of the voltage and current, but also the relative phases...
between the input and output of the circuit is at a minimum (or when the
transfer functionA transfer function is a mathematical representation, in terms of spatial or temporal frequency, of the relation between the input and output of a system. With optical imaging devices, for example, it is the Fourier transform of the point spread function i.e...
is at a maximum). Often this happens when the impedance between the input and output of the circuit is almost zero and when the transfer function is close to one.
Optical resonance
An
optical cavityAn optical cavity or optical resonator is an arrangement of mirrors that forms a standing wave cavity resonator for light waves. Optical cavities are a major component of lasers, surrounding the gain medium and providing feedback of the laser light. They are also used in optical parametric...
or
optical resonator is an arrangement of
mirrorA mirror is an object with at least one polished and therefore specularly reflective surface. The most familiar type of mirror is the plane mirror, which has a flat surface...
s that forms a
standing waveA 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 in opposite...
cavity resonator for light waves. Optical cavities are a major component of
laserA laser is a device that emits light through a process called stimulated emission. Laser light is usually spatially coherent, which means that the light either is emitted in a narrow, low-divergence beam, or can be converted into one with the help of optical components such as lenses...
s, surrounding the gain medium and providing
feedbackFeedback describes the situation when output from an event or phenomenon in the past will influence the same event/phenomenon in the present or future....
of the laser light. They are also used in
optical parametric oscillatorAn optical parametric oscillator is a parametric oscillator which oscillates at optical frequencies. It converts an input laser wave into two output waves of lower frequency by means of nonlinear optical interaction. The sum of the output waves frequencies is equal to the input wave frequency:...
s and some interferometers. Light confined in the cavity reflects multiple times producing
standing waveA 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 in opposite...
s for certain resonance frequencies. The standing wave patterns produced are called modes;
longitudinal modeA longitudinal mode of a resonant cavity is a particular standing wave pattern formed by waves confined in the cavity. The longitudinal modes correspond to the wavelengths of the wave which are reinforced by constructive interference after many reflections from the cavity's reflecting surfaces...
s differ only in frequency while
transverse modeA transverse mode of a beam of electromagnetic radiation is a particular electromagnetic field pattern of radiation measured in a plane perpendicular to the propagation direction of the beam...
s differ for different frequencies and have different intensity patterns across the cross section of the beam.
Ring resonatorsOptical ring resonators consist of a waveguide in a closed loop coupled to one or more input/output waveguides. When light of the appropriate wavelength is coupled to the loop by the input waveguide, it builds up in intensity over multiple round-trips due to constructive interference. It can then...
and whispering galleries are example of optical resonators which do not form standing waves.
Different resonator types are distinguished by the focal lengths of the two mirrors and the distance between them. (Flat mirrors are not often used because of the difficulty of aligning them to the needed precision.) The geometry (resonator type) must be chosen so that the beam remains stable (that the size of the beam does not continually grow with multiple reflections. Resonator types are also designed to meet other criteria such as minimum beam waist or having no focal point (and therefore intense light at that point) inside the cavity.
Optical cavities are designed to have a very large
Q factorIn physics and engineering the quality factor or Q factor is a dimensionless parameter that describes how under-damped an oscillator or resonator is, or equivalently, characterizes a resonator's bandwidth relative to its center frequency....
; a beam will reflect a very large number of times with little
attenuationIn physics, attenuation is the gradual loss in intensity of any kind of flux through a medium. For instance, sunlight is attenuated by dark glasses, and X-rays are attenuated by lead....
. Therefore the frequency line width of the beam is very small indeed compared to the frequency of the laser.
Additional optical resonances are
Guided-mode resonanceGuided-mode resonance or waveguide-mode resonance is a phenomenon wherein the guided modes of an optical waveguide can be excited and simultaneously extracted by the introduction of a phase-matching element such as a diffraction grating or prism...
s and surface plasmon resonance, which result in anomalus reflection and high evanescent fields at resonance. In this case the resonant modes are guided modes of a waveguide or surface plasmon modes of a dielectric-metalic interface. These modes are ususally excited by a subwavelength grating.
Orbital resonance
In
celestial mechanicsCelestial mechanics is the branch of astronomy that deals with the motions of celestial objects. The field applies principles of physics, historically classical mechanics, to astronomical objects such as stars and planets to produce ephemeris data. Orbital mechanics is a subfield which focuses on...
, an
orbital resonanceIn celestial mechanics, an orbital resonance occurs when two orbiting bodies exert a regular, periodic gravitational influence on each other, usually due to their orbital periods being related by a ratio of two small integers. Orbital resonances greatly enhance the mutual gravitational influence of...
occurs when two
orbitIn physics, an orbit is the gravitationally curved path of one object around a point or another body, for example the gravitational orbit of a planet around a star....
ing bodies exert a regular, periodic gravitational influence on each other, usually due to their
orbital periodThe orbital period is the time taken for a given object to make one complete orbit about another object.When mentioned without further qualification in astronomy this refers to the sidereal period of an astronomical object, which is calculated with respect to the stars.There are several kinds of...
s being related by a ratio of two small integers. Orbital resonances greatly enhance the mutual gravitational influence of the bodies. In most cases, this results in an
unstable interaction, in which the bodies exchange momentum and shift orbits until the resonance no longer exists. Under some circumstances, a resonant system can be stable and self correcting, so that the bodies remain in resonance. Examples are the 1:2:4 resonance of
JupiterJupiter is the fifth planet from the Sun and the largest planet within the Solar System. It is a gas giant with a mass slightly less than one-thousandth that of the Sun but is two and a half times the mass of all of the other planets in our Solar System combined. Jupiter is classified as a gas...
's moons
GanymedeGanymede is a moon of Jupiter and the largest moon in the Solar System. Completing an orbit in roughly seven days, it is the seventh moon and third Galilean moon from Jupiter. Ganymede participates in a 1:2:4 orbital resonance with the moons Europa and Io, respectively. It is larger in diameter...
,
EuropaEuropa is the sixth moon of the planet Jupiter. Europa was discovered in 1610 by Galileo Galilei , and named after a mythical Phoenician noblewoman, Europa, who was courted by Zeus and became the queen of Crete...
, and
IoIo is the innermost of the four Galilean moons of the planet Jupiter and, with a diameter of 3,642 kilometres, the fourth-largest moon in the Solar System. It was named after Io, a priestess of Hera who became one of the lovers of Zeus.With over 400 active volcanoes, Io is the most...
, and the 2:3 resonance between
PlutoPluto, formal designation 134340 Pluto, is the second-largest known dwarf planet in the Solar System and the tenth-largest body observed directly orbiting the Sun...
and
NeptuneNeptune is the eighth planet from the Sun in our Solar System. Named for the Roman god of the sea, it is the fourth-largest planet by diameter and the third-largest by mass. Neptune is 17 times the mass of Earth and is slightly more massive than its near-twin Uranus, which is 15 Earth masses and...
. Unstable resonances with
SaturnSaturn is the sixth planet from the Sun and the second largest planet in the Solar System, after Jupiter. Saturn, along with Jupiter, Uranus and Neptune, is classified as a gas giant...
's inner moons give rise to gaps in the
rings of SaturnThe rings of Saturn are the most extensive planetary ring system of any planet in the Solar System. They consist of countless small particles, ranging in size from micrometres to metres, that form clumps that in turn orbit about Saturn...
. The special case of 1:1 resonance (between bodies with similar orbital radii) causes large Solar System bodies to clear the neighborhood around their orbits by ejecting nearly everything else around them; this effect is used in the current
definition of a planetFrom its beginnings denoting the "wandering stars" of the classical world, the definition of "planet" has been fraught with ambiguity. In its long life, the word has meant many different things, often simultaneously...
.
Atomic, particle, and molecular resonance
Nuclear magnetic resonanceNuclear magnetic resonance is a property that magnetic nuclei have in a magnetic field and applied electromagnetic pulse, which cause the nuclei to absorb energy from the EM pulse and radiate this energy back out...
(
NMR) is the name given to a physical resonance phenomenon involving the observation of specific
quantum mechanicalQuantum mechanics is a set of principles describing the physical reality at the atomic level of matter and the subatomic . These descriptions include the simultaneous wave-like and particle-like behavior of both matter and radiation...
magneticIn physics, the term magnetism is used to describe how materials respond on the microscopic level to an applied magnetic field; to categorize the magnetic phase of a material. For example, the most well known form of magnetism is ferromagnetism such that some ferromagnetic materials produce their...
properties of an
atomThe atom is a basic unit of matter consisting of a dense, central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...
ic
nucleusThe nucleus is the very dense region consisting of nucleons at the center of an atom. Almost all of the mass in an atom is made up from the protons and neutrons in the nucleus, with a very small contribution from the orbiting electrons....
in the presence of an applied, external magnetic field. Many scientific techniques exploit NMR phenomena to study
molecular physicsMolecular physics is the study of the physical properties of molecules and of the chemical bonds between atoms that bind them. Its most important experimental techniques are the various types of spectroscopy...
,
crystalCrystallography is the experimental science of determining the arrangement of atoms in solids. In older usage, it is the scientific study of crystals...
s and non-crystalline materials through
NMR spectroscopyNuclear magnetic resonance spectroscopy, most commonly known as NMR spectroscopy, is the name given to a technique which exploits the magnetic properties of certain nuclei. This phenomenon and its origins are detailed in a separate section on nuclear magnetic resonance. The most important...
. NMR is also routinely used in advanced medical imaging techniques, such as in
magnetic resonance imagingMagnetic Resonance Imaging , or nuclear magnetic resonance imaging , is primarily a medical imaging technique most commonly used in radiology to visualize the internal structure and function of the body...
(MRI).
All nuclei that contain odd numbers of
nucleonIn physics, a nucleon is a collective name for two baryons: the neutron and the proton. They are constituents of the atomic nucleus and until the 1960s were thought to be elementary particles. In those days their interactions defined strong interactions. Now they are known to be composite...
s have an intrinsic
magnetic momentThe magnetic moment of a system is a measure of the strength and the direction of its magnetism. More technically , the term magnetic moment of a system usually refers to its magnetic dipole moment, and quantifies the contribution...
and
angular momentumAngular momentum is a quantity that is useful in describing the rotational state of a physical system. For a rigid body rotating around an axis of symmetry , the angular momentum can be expressed as the product of the body's moment of inertia and its angular velocity...
. A key feature of NMR is that the resonance frequency of a particular substance is directly proportional to the strength of the applied magnetic field. It is this feature that is exploited in imaging techniques; if a sample is placed in a non-uniform magnetic field then the resonance frequencies of the sample's nuclei depend on where in the field they are located. Therefore, the particle can be located quite precisely from its resonance frequency.
Electron paramagnetic resonanceElectron paramagnetic resonance or electron spin resonance spectroscopyis a technique for studying chemical species that have one or more unpaired electrons, such as organic and inorganic free radicals or inorganic complexes possessing a transition metal ion...
, otherwise known as
Electron Spin Resonance (ESR) is a spectroscopic technique similar to NMR used with unpaired electrons instead. Materials for which this can be applied are much more limited since the material needs to both have an unpaired spin and be paramagnetic.
The
Mössbauer effectThe Mössbauer effect is a physical phenomenon discovered by the German physicist Rudolf Mößbauer in 1957, and refers to the resonant and recoil-free emission and absorption of gamma ray photons by atoms bound in a solid form...
is a physical phenomenon discovered by
Rudolf MößbauerRudolf Ludwig Mössbauer ; born January 31, 1929) is a German physicist who studied gamma rays from nuclear transitions.Mössbauer was born in Munich, where he also studied physics at the Technical University of Munich and did his PhD with Heinz Maier-Leibnitz...
in 1957; it refers to the resonant and
recoilRecoil is the 'kick' given by a gun when it is fired. In technical terms, this kick is caused by the gun's backward momentum, which exactly balances the forward momentum of the projectile...
-free emission and absorption of
gamma rayGamma rays are electromagnetic radiation of high frequency . They are produced by sub-atomic particle interactions, such as electron-positron annihilation, neutral pion decay, radioactive decay, fusion, fission or inverse Compton scattering in astrophysical processes...
photons by atoms bound in a solid form.
Resonance (particle physics)In particle physics, a resonance is the peak located around a certain energy found in differential cross sections of scattering experiments. These peaks are associated with subatomic particles and their excitations...
: In
quantum mechanicsQuantum mechanics is a set of principles describing the physical reality at the atomic level of matter and the subatomic . These descriptions include the simultaneous wave-like and particle-like behavior of both matter and radiation...
and
quantum field theoryQuantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically described by fields or of many-body systems. It is widely used in particle physics and condensed matter physics...
resonances may appear in similar circumstances to classical physics. However, they can also be thought of as unstable particles, with the formula above still valid if the is the decay rate and replaced by the particle's mass M. In that case, the formula just comes from the particle's
propagatorIn quantum mechanics and quantum field theory, the propagator gives the probability amplitude for a particle to travel from one place to another in a given time, or to travel with a certain energy and momentum. Propagators are used to represent the contribution of virtual particles on the internal...
, with its mass replaced by the
complex numberA complex number, in mathematics, is a number comprising a real number and an imaginary number; it can be written in the form a + bi, where a and b are real numbers, and i is the standard imaginary unit, having the property that i
2 = −1...
. The formula is further related to the particle's decay rate by the
optical theoremIn physics, the optical theorem is a very general law of wave scattering theory, which relates the forward scattering amplitude to the total cross section of the scatterer. It is usually written in the form...
.
Failure of the original Tacoma Narrows Bridge
The dramatically visible, rhythmic twisting that resulted in the 1940 collapse of "Galloping Gertie," the original Tacoma Narrows Bridge, has sometimes been characterized in physics textbooks as a classical example of resonance; however, this description is misleading. The catastrophic vibrations that destroyed the bridge were not due to simple mechanical resonance, but to a more complicated oscillation between the bridge and the winds passing through it — a phenomenon known as aeroelastic flutter.
Robert H. ScanlanRobert H. Scanlan was a civil and aeronautical engineer who came to be widely recognized as a leader in the analysis of wind effects on large structures. Scanlan created the concept of flutter derivatives to aid in the representation of self-excited forces in theoretical models...
, father of the field of bridge aerodynamics, wrote an article about this misunderstanding.
Resonance causing vibration on the International Space Station
The rocket engines for the
International Space StationThe International Space Station is an internationally developed research facility currently being assembled in Low Earth Orbit. On-orbit construction of the station began in 1998 and is scheduled to be completed by 2011, with operations continuing until at least 2015...
are controlled by
autopilotAn autopilot is a mechanical, electrical, or hydraulic system used to guide a vehicle without assistance from a human being. Most people understand an autopilot to refer specifically to aircraft, but self-steering gear for ships, boats, space craft and missiles are sometimes also called by this...
. Ordinarily the uploaded parameters for controlling the engine control system for the Zvezda module will cause the rocket engines to boost the International Space Station to a higher orbit. The rocket engines are hinge-mounted, and ordinarily the operation is not noticed by the crew. But on January 14, 2009, the uploaded parameters caused the autopilot to swing the rocket engines in larger and larger oscillations, at a 2 second frequency. These oscillations were captured on video, and lasted for 142 seconds.
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