In physics, resonance is the tendency of a system to oscillate at its maximum amplitude, associated with specific frequencies known as the system's resonance frequencies (or resonant frequencies). At these frequencies, even small periodic driving forces can produce large amplitude vibrations, because the system stores vibrational energy. When damping is small, the resonance frequency is approximately equal to the natural frequency of the system, which is the frequency of free vibrations. Resonant phenomena occur with all types of vibrations or waves: there is mechanical resonance, acoustic resonance, electromagnetic resonance, NMR, ESR and resonance of quantum wave functions. Resonant systems can be used to generate vibrations of a specific frequency, or pick out specific frequencies from a complex vibration containing many frequencies.

Resonance was discovered by Galileo Galilei with his investigations of pendulums beginning in 1602.


One familiar example is a playground swing, which acts as a pendulum. 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 phase' 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 waves 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 is produced by resonance on an atomic scale, such as electrons in atoms. Other examples are:

* acoustic resonances of musical instruments and human vocal cords
* the timekeeping mechanisms of all modern clocks and watches: the balance wheel in a mechanical watch and the quartz crystal in a quartz watch
* the tidal resonance of the Bay of Fundy
* orbital resonance as exemplified by some moons of the solar system's gas giants
* the resonance of the basilar membrane in the cochlea of the ear, which enables people to distinguish different frequencies or tones in the sounds they hear.
* electrical resonance of tuned circuits in radios and TVs that allow individual stations to be picked up
* creation of coherent light by optical resonance in a laser cavity
* material resonances in atomic scale are the basis of several spectroscopic techniques that are used in condensed matter physics. Examples include Nuclear Magnetic Resonance, Mössbauer effect, Electron Spin Resonance, and many others.
* the shattering of a crystal wineglass when exposed to a musical tone of the right pitch (its resonance frequency).


A physical system can have as many resonance frequencies as it has degrees of freedom; each degree of freedom can vibrate as a harmonic oscillator. Systems with one degree of freedom, such as a mass on a spring, pendulums, balance wheels, and LC tuned circuits have one resonance frequency. Systems with two degrees of freedom, such as coupled pendulums and resonant transformers 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.

Resonances in quantum mechanics

In quantum mechanics and quantum field theory 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 Γ is the decay rate and Ω replaced by the particle's mass M. In that case, the formula just comes from the particle's propagator, with its mass replaced by the complex number M + iΓ. The formula is further related to the particle's decay rate by the optical theorem.