Resonance describes the phenomenon of increased

amplitude The amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period). The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of a ...

that occurs when the

frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from '' angular frequency''. Frequency is measured in hertz (Hz) which is ...

of an applied

periodic Periodicity or periodic may refer to: Mathematics * Bott periodicity theorem, addresses Bott periodicity: a modulo-8 recurrence relation in the homotopy groups of classical groups * Periodic function, a function whose output contains values t ...

force A force is an influence that can cause an Physical object, object to change its velocity unless counterbalanced by other forces. The concept of force makes the everyday notion of pushing or pulling mathematically precise. Because the Magnitude ...

(or a Fourier component of it) is equal or close to a

natural frequency Natural frequency, also known as eigenfrequency, is the frequency at which a system tends to oscillate in the absence of any driving force. The motion pattern of a system oscillating at its natural frequency is called the normal mode (if all p ...

of the system on which it acts. When an

oscillating Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum ...

force is applied at a resonant frequency of a dynamic system, the system will oscillate at a higher

than when the same force is applied at other, non-resonant frequencies. Frequencies at which the response amplitude is a

relative maximum In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given ra ...

are also known as resonant frequencies or resonance frequencies of the system. Small periodic forces that are near a resonant frequency of the system have the ability to produce large amplitude

oscillation Oscillation is the repetitive or Periodic function, periodic variation, typically in time, of some measure about a central value (often a point of Mechanical equilibrium, equilibrium) or between two or more different states. Familiar examples o ...

s in the system due to the storage of

vibrational energy In physics, sound energy is a form of energy that can be heard by living things. Only those waves that have a frequency of 16 Hz to 20 kHz are audible to humans. However, this range is an average and will slightly change from indivi ...

. Resonance phenomena occur with all types of vibrations or

wave In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (r ...

s: there is

mechanical resonance Mechanical resonance is the tendency of a mechanical system to respond at greater amplitude when the frequency of its oscillations matches the system's natural frequency of vibration (its '' resonance frequency'' or ''resonant frequency'') clos ...

orbital resonance In celestial mechanics, orbital resonance occurs when orbiting bodies exert regular, periodic gravitational influence on each other, usually because their orbital periods are related by a ratio of small integers. Most commonly, this relations ...

acoustic resonance Acoustic resonance is a phenomenon in which an acoustic system amplifies sound waves whose frequency matches one of its own natural frequencies of vibration (its '' resonance frequencies''). The term "acoustic resonance" is sometimes used to na ...

electromagnetic In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of a ...

resonance,

nuclear magnetic resonance Nuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei in a strong constant magnetic field are perturbed by a weak oscillating magnetic field (in the near field) and respond by producing an electromagnetic signal with a ...

(NMR),

electron spin resonance Electron paramagnetic resonance (EPR) or electron spin resonance (ESR) spectroscopy is a method for studying materials that have unpaired electrons. The basic concepts of EPR are analogous to those of nuclear magnetic resonance (NMR), but the s ...

(ESR) and resonance of quantum

wave function A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements m ...

s. Resonant systems can be used to generate vibrations of a specific frequency (e.g.,

musical instrument A musical instrument is a device created or adapted to make musical sounds. In principle, any object that produces sound can be considered a musical instrument—it is through purpose that the object becomes a musical instrument. A person who pl ...

s), or pick out specific frequencies from a complex vibration containing many frequencies (e.g., filters). The term ''resonance'' (from

Latin Latin (, or , ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through the power ...

''resonantia'', 'echo', from ''resonare'', 'resound') originated from the field of acoustics, particularly the

sympathetic resonance Sympathetic resonance or sympathetic vibration is a harmonic phenomenon wherein a passive string or vibratory body responds to external vibrations to which it has a harmonic likeness. The classic example is demonstrated with two similarly-tuned ...

observed in musical instruments, e.g., when one string starts to vibrate and produce sound after a different one is struck.

Overview

Resonance occurs when a system is able to store and easily transfer energy between two or more different

storage mode Storage may refer to: Goods Containers * Dry cask storage, for storing high-level radioactive waste * Food storage * Intermodal container, cargo shipping * Storage tank Facilities * Garage (residential), a storage space normally used to store c ...

s (such as kinetic energy and potential energy in the case of a simple pendulum). However, there are some losses from cycle to cycle, called

damping Damping is an influence within or upon an oscillatory system that has the effect of reducing or preventing its oscillation. In physical systems, damping is produced by processes that dissipate the energy stored in the oscillation. Examples in ...

. When damping is small, the resonant frequency is approximately equal to the

of the system, which is a frequency of unforced vibrations. Some systems have multiple, distinct, resonant frequencies.

Examples

A familiar example is a playground

swing Swing or swinging may refer to: Apparatus * Swing (seat), a hanging seat that swings back and forth * Pendulum, an object that swings * Russian swing, a swing-like circus apparatus * Sex swing, a type of harness for sexual intercourse * Swing rid ...

, which acts as a

pendulum A pendulum is a weight suspended from a wikt:pivot, pivot so that it can swing freely. When a pendulum is displaced sideways from its resting, Mechanical equilibrium, equilibrium position, it is subject to a restoring force due to gravity that ...

. Pushing a person in a swing in time with the natural interval of the swing (its resonant frequency) makes the swing go higher and higher (maximum amplitude), while attempts to push the swing at a faster or slower tempo produce smaller arcs. This is because the energy the swing absorbs is maximized when the pushes match the swing's natural oscillations. Resonance occurs widely in nature, and is exploited in many devices. It is the mechanism by which virtually all

sinusoidal A sine wave, sinusoidal wave, or just sinusoid is a mathematical curve defined in terms of the '' sine'' trigonometric function, of which it is the graph. It is a type of continuous wave and also a smooth periodic function. It occurs often in ...

waves and vibrations are generated. Many sounds we hear, such as when hard objects of

metal A metal (from Greek μέταλλον ''métallon'', "mine, quarry, metal") is a material that, when freshly prepared, polished, or fractured, shows a lustrous appearance, and conducts electricity and heat relatively well. Metals are typi ...

glass Glass is a non-Crystallinity, crystalline, often transparency and translucency, transparent, amorphous solid that has widespread practical, technological, and decorative use in, for example, window panes, tableware, and optics. Glass is most ...

, or

wood Wood is a porous and fibrous structural tissue found in the stems and roots of trees and other woody plants. It is an organic materiala natural composite of cellulose fibers that are strong in tension and embedded in a matrix of ligni ...

are struck, are caused by brief resonant vibrations in the object. Light and other short wavelength

electromagnetic radiation In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible ...

is produced by resonance on an

atomic scale Atomic spacing refers to the distance between the nuclei of atoms in a material. This space is extremely large compared to the size of the atomic nucleus, and is related to the chemical bonds which bind atoms together. In solid materials, the ato ...

, such as

electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary partic ...

s in atoms. Other examples of resonance: * Timekeeping mechanisms of modern clocks and watches, e.g., the

balance wheel A balance wheel, or balance, is the timekeeping device used in mechanical watches and small 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 ...

in a mechanical

watch A watch is a portable timepiece intended to be carried or worn by a person. It is designed to keep a consistent movement despite the motions caused by the person's activities. A wristwatch is designed to be worn around the wrist, attached ...

and the

quartz crystal Quartz is a hard, crystalline mineral composed of silica (silicon dioxide). The atoms are linked in a continuous framework of SiO4 silicon-oxygen tetrahedra, with each oxygen being shared between two tetrahedra, giving an overall chemical form ...

in a

quartz watch Quartz is a hard, crystalline mineral composed of silica (silicon dioxide). The atoms are linked in a continuous framework of SiO4 silicon-oxygen tetrahedra, with each oxygen being shared between two tetrahedra, giving an overall chemical form ...

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. Then an incident tidal wave can be reinforce ...

of the

Bay of Fundy The Bay of Fundy (french: Baie de Fundy) is a bay between the Canadian provinces of New Brunswick and Nova Scotia, with a small portion touching the U.S. state of Maine. It is an arm of the Gulf of Maine. Its extremely high tidal range is th ...