Resonance

# Resonance

Overview
In physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

, resonance is the tendency of a system to oscillate at a greater 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...

at some frequencies
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...

than at others. These are known as the system's resonant frequencies (or resonance frequencies). At these frequencies, even small periodic
Periodic function
In 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 radians. Periodic functions are used throughout science to describe oscillations,...

driving forces can produce large amplitude oscillations, because the system stores vibrational energy.
Discussion

Encyclopedia
In physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

, resonance is the tendency of a system to oscillate at a greater 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...

at some frequencies
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...

than at others. These are known as the system's resonant frequencies (or resonance frequencies). At these frequencies, even small periodic
Periodic function
In 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 radians. Periodic functions are used throughout science to describe oscillations,...

driving forces can produce large amplitude oscillations, because the system stores vibrational energy.

Resonance occurs when a system is able to store and easily transfer energy between two or more different storage modes (such as kinetic energy and potential energy in the case of a pendulum). However, there are some losses from cycle to cycle, called damping
Damping
In 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...

. When damping is small, the resonant frequency is approximately equal to the natural frequency of the system, which is a frequency of unforced vibrations. Some systems have multiple, distinct, resonant frequencies.

Resonance phenomena occur with all types of vibrations or waves
WAVES
The WAVES were a World War II-era division of the U.S. Navy that consisted entirely of women. The name of this group is an acronym for "Women Accepted for Volunteer Emergency Service" ; the word "emergency" implied that the acceptance of women was due to the unusual circumstances of the war and...

: there is mechanical resonance
Mechanical resonance
Mechanical 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 resonance
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....

, electromagnetic
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...

resonance, nuclear magnetic resonance
Nuclear magnetic resonance
Nuclear magnetic resonance is a physical phenomenon in which magnetic nuclei in a magnetic field absorb and re-emit electromagnetic radiation...

(NMR), electron spin resonance
Electron paramagnetic resonance
Electron 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 at a specific frequency (e.g. musical instruments), or pick out specific frequencies from a complex vibration containing many frequencies (e.g. filters).

Resonance was recognized by Galileo Galilei
Galileo Galilei
Galileo 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 pendulum
Pendulum
A pendulum is a weight suspended from a pivot so that 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...

s and musical strings
Strings (music)
A string is the vibrating element that produces sound in string instruments, such as the guitar, harp, piano, and members of the violin family. Strings are lengths of a flexible material kept under tension so that they may vibrate freely, but controllably. Strings may be "plain"...

beginning in 1602.

## Examples

One familiar example is a playground swing
Swing (seat)
A swing is a hanging seat, usually found at playgrounds for children, a circus for acrobats, or on a porch for relaxing. The seat of a swing may be suspended from chains or ropes. Once a swing is in motion it continues to oscillate like a pendulum until external interference or drag brings it to a...

, which acts as a pendulum
Pendulum
A pendulum is a weight suspended from a pivot so that 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...

. Pushing a person in a swing in time with the natural interval of the swing (its resonant 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 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:...

' 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 wave
Wave
In physics, a wave is a disturbance that travels through space and time, accompanied by the transfer of energy.Waves travel and the wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium—that is, with little or no associated mass...

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 radiation
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...

is produced by resonance on an atomic scale, such as electrons in atoms. Other examples are:

Mechanical
Mechanical resonance
Mechanical 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 resonance
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....

• the timekeeping mechanisms of all modern clocks and watches: the balance wheel
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 watch
Watch
A watch is a small timepiece, typically worn either on the wrist or attached on a chain and carried in a pocket, with wristwatches being the most common type of watch used today. They evolved in the 17th century from spring powered clocks, which appeared in the 15th century. The first watches were...

and the quartz crystal in a quartz watch
• the tidal resonance
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 Fundy
Bay of Fundy
The 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
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 shattering of a crystal wineglass when exposed to a musical tone of the right pitch (its resonant frequency)

Electrical resonance
Electrical resonance
Electrical resonance occurs in an electric circuit at a particular resonance frequency where the imaginary parts of circuit element impedances or admittances cancel each other...

• electrical resonance
Electrical resonance
Electrical resonance occurs in an electric circuit at a particular resonance frequency where the imaginary parts of circuit element impedances or admittances cancel each other...

Radio is the transmission of signals through free space 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 resonance
Optical cavity
An 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
Coherence (physics)
In physics, coherence is a property of waves that enables stationary interference. More generally, coherence describes all properties of the correlation between physical quantities of a wave....

light by optical resonance in a laser
Laser
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of photons. The term "laser" originated as an acronym for Light Amplification by Stimulated Emission of Radiation...

cavity
Optical cavity
An 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 resonance
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...

in astronomy
Astronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...

• orbital resonance
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 moons
Natural satellite
A natural satellite or moon is a celestial body that orbits a planet or smaller body, which is called its primary. The two terms are used synonymously for non-artificial satellites of planets, of dwarf planets, and of minor planets....

of the solar system
Solar System
The Solar System consists of the Sun and the astronomical objects gravitationally bound in orbit around it, all of which formed from the collapse of a giant molecular cloud approximately 4.6 billion years ago. The vast majority of the system's mass is in the Sun...

's gas giants
Gas Giants
Gas 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
Spectroscopy is the study of the interaction between matter and radiated energy. Historically, spectroscopy originated through the study of visible light dispersed according to its wavelength, e.g., by a prism. Later the concept was expanded greatly to comprise any interaction with radiative...

techniques that are used in condensed matter physics
Condensed matter physics
Condensed matter physics deals with the physical properties of condensed phases of matter. These properties appear when a number of atoms at the supramolecular and macromolecular scale interact strongly and adhere to each other or are otherwise highly concentrated in a system. The most familiar...

.
• Nuclear Magnetic Resonance
Nuclear magnetic resonance
Nuclear magnetic resonance is a physical phenomenon in which magnetic nuclei in a magnetic field absorb and re-emit electromagnetic radiation...

• Mössbauer effect
Mössbauer effect
The Mössbauer effect, or recoilless nuclear resonance fluorescence‎, is a physical phenomenon discovered by Rudolf Mössbauer in 1958. It involves the resonant and recoil-free emission and absorption of γ radiation by atomic nuclei bound in a solid...

• 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 damped
Damping
In 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 damping
Harmonic oscillator
In classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force, F, proportional to the displacement, x: \vec F = -k \vec x \, 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 proportional
Proportionality (mathematics)
In mathematics, two variable quantities are proportional if one of them is always the product of the other and a constant quantity, called the coefficient of proportionality or proportionality constant. In other words, are proportional if the ratio \tfrac yx is constant. We also say that one...

to the Q factor
Q factor
In 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 engineering
Electrical engineering
Electrical engineering is a field of engineering that generally deals with the study and application of electricity, electronics and electromagnetism. The field first became an identifiable occupation in the late nineteenth century after commercialization of the electric telegraph and electrical...

, this approximate symmetric response is known as the universal resonance curve, a concept introduced by Frederick E. Terman in 1932 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 resonant frequencies as it has degrees of freedom
Degrees of freedom (engineering)
In 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 oscillator
Harmonic oscillator
In classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force, F, proportional to the displacement, x: \vec F = -k \vec x \, where k is a positive constant....

. Systems with one degree of freedom, such as a mass on a spring, pendulum
Pendulum
A pendulum is a weight suspended from a pivot so that 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...

s, balance wheel
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...

s, and LC tuned circuits
RLC circuit
An RLC circuit is an electrical circuit consisting of a resistor, an inductor, and a capacitor, connected in series or in parallel. The RLC part of the name is due to those letters being the usual electrical symbols for resistance, inductance and capacitance respectively...

have one resonant frequency. Systems with two degrees of freedom, such as coupled pendulums
Double pendulum
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 behavior with a strong sensitivity to initial conditions. The motion of a double pendulum is governed by a set of...

and resonant transformers can have two resonant 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 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...

s, 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....

s, quartz crystals, microwave
Microwave
Microwaves, a subset of radio waves, have wavelengths ranging from as long as one meter to as short as one millimeter, or equivalently, with frequencies between 300 MHz and 300 GHz. This broad definition includes both UHF and EHF , and various sources use different boundaries...

cavities, and laser
Laser
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of photons. The term "laser" originated as an acronym for Light Amplification by Stimulated Emission of Radiation...

rods. Since these can be viewed as being made of millions of coupled moving parts (such as atoms), they can have millions of resonant 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 integer number of wavelengths of the wave:

If the velocity of a wave is , the frequency is so the resonant frequencies are:

So the resonant frequencies of resonators, called normal modes, are equally spaced multiples of a lowest frequency called the fundamental frequency
Fundamental frequency
The fundamental frequency, often referred to simply as the fundamental and abbreviated f0, is defined as the lowest frequency of a periodic waveform. In terms of a superposition of sinusoids The fundamental frequency, often referred to simply as the fundamental and abbreviated f0, is defined as the...

. The multiples are often called 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...

s. There may be several such series of resonant frequencies, corresponding to different modes of vibration.

## Q factor

The quality factor or Q factor is a dimensionless
Dimensionless quantity
In dimensional analysis, a dimensionless quantity or quantity of dimension one is a quantity without an associated physical dimension. It is thus a "pure" number, and as such always has a dimension of 1. Dimensionless quantities are widely used in mathematics, physics, engineering, economics, and...

parameter that describes how under-damped
Damping
In 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...

an oscillator
Oscillation
Oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. Familiar examples include a swinging pendulum and AC power. The term vibration is sometimes used more narrowly to mean a mechanical oscillation but sometimes...

or 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...

is, or equivalently, characterizes a resonator's bandwidth relative to its center frequency.
Higher Q indicates a lower rate of energy loss relative to the stored energy of the oscillator, i.e. the oscillations die out more slowly. A pendulum suspended from a high-quality bearing, oscillating in air, has a high Q, while a pendulum immersed in oil has a low Q. Oscillators with high quality factors have low damping
Damping
In 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...

which tends to make them ring longer.

Sinusoidally
Sine wave
The sine wave or sinusoid is a mathematical function that describes a smooth repetitive oscillation. It occurs often in pure mathematics, as well as physics, signal processing, electrical engineering and many other fields...

driven 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...

s having higher Q factors resonate with greater amplitudes (at the resonant frequency) but have a smaller range of frequencies around the frequency at which they resonate. The range of frequencies at which the oscillator resonates is called the bandwidth. Thus, a high Q tuned circuit
RLC circuit
An RLC circuit is an electrical circuit consisting of a resistor, an inductor, and a capacitor, connected in series or in parallel. The RLC part of the name is due to those letters being the usual electrical symbols for resistance, inductance and capacitance respectively...

in a radio receiver would be more difficult to tune, but would have greater selectivity, it would do a better job of filtering out signals from other stations that lie nearby on the spectrum. High Q oscillators operate over a smaller range of frequencies and are more stable. (See oscillator phase noise
Oscillator Phase Noise
Oscillators inherently produce high levels of phase noise. That noise increases at frequencies close to the oscillation frequency or its harmonics. With the noise being close to the oscillation frequency, it cannot be removed by filtering without also removing the oscillation signal...

.)

The quality factor of oscillators vary substantially from system to system. Systems for which damping is important (such as dampers keeping a door from slamming shut) have Q = ½. Clocks, lasers, and other systems that need either strong resonance or high frequency stability need high quality factors. Tuning forks have quality factors around Q = 1000. The quality factor of atomic clock
Atomic clock
An atomic clock is a clock that uses an electronic transition frequency in the microwave, optical, or ultraviolet region of the electromagnetic spectrum of atoms as a frequency standard for its timekeeping element...

s and some high-Q lasers
Optical cavity
An 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...

can reach as high as 1011 and higher.

There are many alternate quantities used by physicists and engineers to describe how damped an oscillator is that are closely related to its quality factor. Important examples include: the damping ratio
Damping ratio
[[Image:Damped spring.gif|right|frame|Underdamped [[spring–mass system]] with ζ 1 , and is referred to as overdamped.*Underdamped:If s is a complex number, then the solution is a decaying exponential combined with an oscillatory portion that looks like \exp...

, relative bandwidth, linewidth
Oscillator linewidth
The concept of a linewidth is borrowed from laser spectroscopy. The linewidth of a laser is a measure of its phase noise. The spectrogram of a laser is produced by passing its light through a prism. The spectrogram of the output of a pure noise-free laser will consist of a single infinitely thin...

and bandwidth measured in octave
Octave (electronics)
In electronics, an octave is a doubling or halving of a frequency. The term is derived from the musical octave which similarly describes such frequency ratios, but the prefix octa-, denoting eight, has no significance in physics...

s.

### Mechanical and acoustic resonance

Mechanical resonance is the tendency of a mechanical system
Mechanics
Mechanics is the branch of physics concerned with the behavior of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment....

to absorb more energy when the 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...

of its oscillations matches the system's natural frequency of vibration
Vibration
Vibration 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, trains, and aircraft. When designing objects, Engineer
Engineer
An engineer is a professional practitioner of engineering, concerned with applying scientific knowledge, mathematics and ingenuity to develop solutions for technical problems. Engineers design materials, structures, machines and systems while considering the limitations imposed by practicality,...

s must ensure the mechanical resonant frequencies of the component parts do not match driving vibrational frequencies of motors or other oscillating parts, a phenomenon known as resonance disaster.

Avoiding resonance disasters is a major concern in every building, tower and bridge construction
Construction
In 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 human multitasking...

project. As a countermeasure, shock mounts can be installed to absorb resonant frequencies and thus dissipate the absorbed energy. The Taipei 101
Taipei 101
Taipei 101 , formerly known as the Taipei World Financial Center, is a landmark skyscraper located in Xinyi District, Taipei, Taiwan. The building ranked officially as the world's tallest from 2004 until the opening of the Burj Khalifa in Dubai in 2010...

building relies on a 660 tonnes (727.5 ST) — a tuned mass damper
Tuned mass damper
A tuned mass damper, also known as an active mass damper or harmonic absorber, is a device mounted in structures to reduce the amplitude of mechanical vibrations. Their application can prevent discomfort, damage, or outright structural failure...

— 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, engineer
Engineer
An engineer is a professional practitioner of engineering, concerned with applying scientific knowledge, mathematics and ingenuity to develop solutions for technical problems. Engineers design materials, structures, machines and systems while considering the limitations imposed by practicality,...

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 clock
Clock
A clock is an instrument used to indicate, keep, and co-ordinate time. The word clock is derived ultimately from the Celtic words clagan and clocca meaning "bell". A silent instrument missing such a mechanism has traditionally been known as a timepiece...

s keep time by mechanical resonance in a balance wheel
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...

, pendulum
Pendulum
A pendulum is a weight suspended from a pivot so that 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...

, or quartz crystal
Quartz clock
A 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 resonance
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....

is a branch of mechanical resonance
Mechanical resonance
Mechanical 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 with the mechanical vibrations across the frequency range of human hearing, in other words sound
Sound
Sound is a mechanical wave that 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.-Propagation of...

. For humans, hearing is normally limited to frequencies between about 20 Hz
Hertz
The hertz is the SI unit of frequency defined as the number of cycles per second of a periodic phenomenon. One of its most common uses is the description of the sine wave, particularly those used in radio and audio applications....

and 20,000 Hz (20 kHz),

Acoustic resonance is an important consideration for instrument builders, as most acoustic instruments
Musical instrument
A musical instrument is a device created or adapted for the purpose of making musical sounds. In principle, any object that produces sound can serve as a musical instrument—it is through purpose that the object becomes a musical instrument. The history of musical instruments dates back to the...

use 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...

s, such as the strings and body of a violin
Violin
The violin is a string instrument, usually with four strings tuned in perfect fifths. It is the smallest, highest-pitched member of the violin family of string instruments, which includes the viola and cello....

, the length of tube in a flute
Flute
The flute is a musical instrument of the woodwind family. 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, and tension on, a drum membrane.

Like mechanical resonance, acoustic resonance can result in catastrophic failure of the object at resonance. 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 circuit
Electrical network
An electrical network is an interconnection of electrical elements such as resistors, inductors, capacitors, transmission lines, voltage sources, current sources and switches. An electrical circuit is a special type of network, one that has a closed loop giving a return path for the current...

at a particular resonant frequency when the impedance
Electrical impedance
Electrical impedance, or simply impedance, is the measure of the opposition that an electrical circuit presents to the passage of a current when a voltage is applied. In quantitative terms, it is the complex ratio of the voltage to the current in an alternating current circuit...

of the circuit is at a minimum in a series circuit or at maximum in a parallel circuit (or when the transfer function
Transfer function
A transfer function is a mathematical representation, in terms of spatial or temporal frequency, of the relation between the input and output of a linear time-invariant system. With optical imaging devices, for example, it is the Fourier transform of the point spread function i.e...

is at a maximum).

### Optical resonance

An optical cavity
Optical cavity
An 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 mirror
Mirror
A mirror is an object that reflects light or sound in a way that preserves much of its original quality prior to its contact with the mirror. Some mirrors also filter out some wavelengths, while preserving other wavelengths in the reflection...

s that forms 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...

cavity resonator for light waves. Optical cavities are a major component of laser
Laser
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of photons. The term "laser" originated as an acronym for Light Amplification by Stimulated Emission of Radiation...

s, surrounding the gain medium and providing feedback
Feedback
Feedback describes the situation when output from an event or phenomenon in the past will influence an occurrence or occurrences of the same Feedback describes the situation when output from (or information about the result of) an event or phenomenon in the past will influence an occurrence or...

of the laser light. They are also used in optical parametric oscillator
Optical parametric oscillator
An 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 second order nonlinear optical interaction. The sum of the output waves frequencies is equal to the input wave...

s and some interferometers. Light confined in the cavity reflects multiple times producing 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 for certain resonant frequencies. The standing wave patterns produced are called modes. Longitudinal mode
Longitudinal mode
For the longitudinal mode of conduction of electric currents, see Common 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...

s differ only in frequency while transverse mode
Transverse mode
A 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 resonators
Optical ring resonators
An optical ring resonator is a set of three or more waveguides in which at least one is a closed loop coupled to one input waveguide and one output waveguides...

and whispering galleries are examples of optical resonators that 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 precisely.) The geometry (resonator type) must be chosen so the beam remains stable, i.e. the beam size does not continue to grow with each reflection. 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 factor
Q factor
In 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 attenuation
Attenuation
In physics, attenuation is the gradual loss in intensity of any kind of flux through a medium. For instance, sunlight is attenuated by dark glasses, X-rays are attenuated by lead, and light and sound are attenuated by water.In electrical engineering and telecommunications, attenuation affects the...

. Therefore the frequency line width of the beam is very small compared to the frequency of the laser.

Additional optical resonances are guided-mode resonance
Guided-mode resonance
Guided-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-metallic interface. These modes are usually excited by a subwavelength grating.

### Orbital resonance

In celestial mechanics
Celestial mechanics
Celestial 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 resonance
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...

occurs when two orbit
Orbit
In physics, an orbit is the gravitationally curved path of an object around a point in space, for example the orbit of a planet around the center of a star system, such as the Solar System...

ing bodies exert a regular, periodic gravitational influence on each other, usually due to their orbital period
Orbital period
The 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 Jupiter
Jupiter
Jupiter is the fifth planet from the Sun and the largest planet within the Solar System. It is a gas giant with mass one-thousandth that of the Sun but is two and a half times the mass of all the other planets in our Solar System combined. Jupiter is classified as a gas giant along with Saturn,...

's moons Ganymede
Ganymede (moon)
Ganymede is a satellite of Jupiter and the largest moon in the Solar System. It is the seventh moon and third Galilean satellite outward from Jupiter. Completing an orbit in roughly seven days, Ganymede participates in a 1:2:4 orbital resonance with the moons Europa and Io, respectively...

, Europa
Europa (moon)
Europa Slightly smaller than Earth's Moon, Europa is primarily made of silicate rock and probably has an iron core. It has a tenuous atmosphere composed primarily of oxygen. Its surface is composed of ice and is one of the smoothest in the Solar System. This surface is striated by cracks and...

, and Io
Io (moon)
Io ) is the innermost of the four Galilean moons of the planet Jupiter and, with a diameter of , the fourth-largest moon in the Solar System. It was named after the mythological character of Io, a priestess of Hera who became one of the lovers of Zeus....

, and the 2:3 resonance between Pluto
Pluto
Pluto, formal designation 134340 Pluto, is the second-most-massive known dwarf planet in the Solar System and the tenth-most-massive body observed directly orbiting the Sun...

and Neptune
Neptune
Neptune is the eighth and farthest planet from the Sun in the 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 times...

. Unstable resonances with Saturn
Saturn
Saturn is the sixth planet from the Sun and the second largest planet in the Solar System, after Jupiter. Saturn is named after the Roman god Saturn, equated to the Greek Cronus , the Babylonian Ninurta and the Hindu Shani. Saturn's astronomical symbol represents the Roman god's sickle.Saturn,...

's inner moons give rise to gaps in the rings of Saturn
Rings of Saturn
The 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 planet
Definition of planet
The definition of planet, since the word was coined by the ancient Greeks, has included within its scope a wide range of celestial bodies. Greek astronomers employed the term asteres planetai , "wandering stars", for objects which apparently move over the sky...

.

### Atomic, particle, and molecular resonance

Nuclear magnetic resonance
Nuclear magnetic resonance
Nuclear magnetic resonance is a physical phenomenon in which magnetic nuclei in a magnetic field absorb and re-emit electromagnetic radiation...

(NMR) is the name given to a physical resonance phenomenon involving the observation of specific 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...

magnetic
Magnetism
Magnetism is a property of materials that respond at an atomic or subatomic level to an applied magnetic field. Ferromagnetism is the strongest and most familiar type of magnetism. It is responsible for the behavior of permanent magnets, which produce their own persistent magnetic fields, as well...

properties of an atom
Atom
The atom is a basic unit of matter that consists 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 nucleus
Atomic nucleus
The nucleus is the very dense region consisting of protons and neutrons at the center of an atom. It was discovered in 1911, as a result of Ernest Rutherford's interpretation of the famous 1909 Rutherford experiment performed by Hans Geiger and Ernest Marsden, under the direction of Rutherford. The...

in the presence of an applied, external magnetic field. Many scientific techniques exploit NMR phenomena to study molecular physics
Molecular physics
Molecular physics is the study of the physical properties of molecules, the chemical bonds between atoms as well as the molecular dynamics. Its most important experimental techniques are the various types of spectroscopy...

, crystal
Crystallography
Crystallography is the experimental science of the arrangement of atoms in solids. The word "crystallography" derives from the Greek words crystallon = cold drop / frozen drop, with its meaning extending to all solids with some degree of transparency, and grapho = write.Before the development of...

s and non-crystalline materials through NMR spectroscopy
NMR spectroscopy
Nuclear magnetic resonance spectroscopy, most commonly known as NMR spectroscopy, is a research technique that exploits the magnetic properties of certain atomic nuclei to determine physical and chemical properties of atoms or the molecules in which they are contained...

. NMR is also routinely used in advanced medical imaging techniques, such as in magnetic resonance imaging
Magnetic resonance imaging
Magnetic resonance imaging , nuclear magnetic resonance imaging , or magnetic resonance tomography is a medical imaging technique used in radiology to visualize detailed internal structures...

(MRI).

All nuclei containing odd numbers of nucleon
Nucleon
In physics, a nucleon is a collective name for two particles: the neutron and the proton. These are the two constituents of the atomic nucleus. Until the 1960s, the nucleons were thought to be elementary particles...

s have an intrinsic magnetic moment
Magnetic moment
The magnetic moment of a magnet is a quantity that determines the force that the magnet can exert on electric currents and the torque that a magnetic field will exert on it...

and angular momentum
Angular momentum
In physics, angular momentum, moment of momentum, or rotational momentum is a conserved vector quantity that can be used to describe the overall state of a physical system...

. A key feature of NMR is that the resonant 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 resonant frequencies of the sample's nuclei depend on where in the field they are located. Therefore, the particle can be located quite precisely by its resonant frequency.

Electron paramagnetic resonance
Electron paramagnetic resonance
Electron 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, but uses 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 effect
Mössbauer effect
The Mössbauer effect, or recoilless nuclear resonance fluorescence‎, is a physical phenomenon discovered by Rudolf Mössbauer in 1958. It involves the resonant and recoil-free emission and absorption of γ radiation by atomic nuclei bound in a solid...

is the resonant and recoil
Recoil
Recoil is the backward momentum of a gun when it is discharged. In technical terms, the recoil caused by the gun exactly balances the forward momentum of the projectile and exhaust gasses, according to Newton's third law...

-free emission and absorption of gamma ray
Gamma ray
Gamma radiation, also known as gamma rays or hyphenated as gamma-rays and denoted as γ, is electromagnetic radiation of high frequency . Gamma rays are usually naturally produced on Earth by decay of high energy states in atomic nuclei...

photons by atoms bound in a solid form.

Resonance (particle physics)
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 mechanics
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...

and quantum field theory
Quantum field theory
Quantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...

resonances may appear in similar circumstances to classical physics. However, they can also be thought of as unstable particles, with the formula above valid if the is the decay rate and replaced by the particle's mass M. In that case, the formula comes from the particle's propagator, with its mass replaced by the complex number
Complex number
A complex number is a number consisting of a real part and an imaginary part. Complex numbers extend the idea of the one-dimensional number line to the two-dimensional complex plane by using the number line for the real part and adding a vertical axis to plot the imaginary part...

. The formula is further related to the particle's decay rate by the optical theorem
Optical theorem
In physics, the optical theorem is a general law of wave scattering theory, which relates the forward scattering amplitude to the total cross section of the scatterer...

.

### 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 interaction between the bridge and the winds passing through it — a phenomenon known as aeroelastic flutter. Robert H. Scanlan
Robert H. Scanlan
Robert 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...

### Resonance causing a vibration on the International Space Station

The rocket engines for the International Space Station
International Space Station
The International Space Station is a habitable, artificial satellite in low Earth orbit. The ISS follows the Salyut, Almaz, Cosmos, Skylab, and Mir space stations, as the 11th space station launched, not including the Genesis I and II prototypes...

are controlled by autopilot
Autopilot
An autopilot is a mechanical, electrical, or hydraulic system used to guide a vehicle without assistance from a human being. An autopilot can refer specifically to aircraft, self-steering gear for boats, or auto guidance of space craft and missiles...

. 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 frequency of 0.5 Hz. These oscillations were captured on video, and lasted for 142 seconds.

• Definition of Resonance - "The increase in amplitude of oscillation of an electric or mechanical system exposed to a periodic force whose frequency is equal or very close to the natural undamped frequency of the system."
• Resonance - a chapter from an online textbook
• Greene, Brian
Brian Greene
Brian Greene is an American theoretical physicist and string theorist. He has been a professor at Columbia University since 1996. Greene has worked on mirror symmetry, relating two different Calabi-Yau manifolds...

, "Resonance in strings". The Elegant Universe
The Elegant Universe
The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory is a book by Brian Greene published in 1999, which introduces string and superstring theory, and provides a comprehensive though non-technical assessment of the theory and some of its shortcomings...

, NOVA (PBS