This article is about resonance in physics. For other senses of this term, see resonance (disambiguation).

Increase of amplitude as damping decreases and frequency approaches resonance frequency ^[1]

In physics, resonance is the tendency of a system to oscillate at maximum amplitude at certain frequencies, known as the system's resonance frequencies (or resonant frequencies). Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. Oscillation is the repetitive variation typically in Time, of some measure about a central value (often a point of Equilibrium) or between two or more different states Amplitude is the magnitude of change in the oscillating variable with each Oscillation, within an oscillating system Frequency is a measure of the number of occurrences of a repeating event per unit Time. At these frequencies, even small periodic driving forces can produce large amplitude vibrations, because the system stores vibrational energy. In Mathematics, a periodic function is a function that repeats its values after some definite period has been added to its Independent variable When damping is small, the resonance frequency is approximately equal to the natural frequency of the system, which is the frequency of free vibrations. Damping is any effect either deliberately engendered or inherent to a system that tends to reduce the amplitude of Oscillations of an oscillatory system The fundamental tone, often referred to simply as the fundamental and abbreviated fo, is the lowest frequency in a harmonic series. Resonant phenomena occur with all type of vibrations or waves; mechanical (acoustic), electromagnetic, and quantum wave functions. Electromagnetic radiation takes the form of self-propagating Waves in a Vacuum or in Matter. A wave function or wavefunction is a mathematical tool used in Quantum mechanics to describe any physical system 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. Galileo Galilei (15 February 1564 &ndash 8 January 1642 was a Tuscan ( Italian) Physicist, Mathematician, Astronomer, and Philosopher A pendulum is a mass that is attached to a pivot from which it can swing freely

Examples

One familiar example is a playground swing, which acts as a pendulum. A swing is a hanging seat usually found in a Playground for children a Circus for Acrobats or on a Porch for relaxing A pendulum is a mass that is attached to a pivot from which it can swing freely 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. Sinusoidal waves are usually generated by resonance. A wave is a disturbance that propagates through Space and Time, usually with transference of Energy. 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. Electromagnetic radiation takes the form of self-propagating Waves in a Vacuum or in Matter. Other examples are:

• acoustic resonances of musical instruments and our vocal cords
• the oscillations of the balance wheel in a mechanical 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. Acoustic resonance is the tendency of an acoustic system to absorb more energy when the Frequency of its oscillations matches the system's natural frequency of vibration A musical instrument is a device constructed or modified for the purpose of making Music. The vocal folds, also known commonly as vocal cords, are composed of twin infoldings of Mucous membrane stretched horizontally across the Larynx. The balance wheel is the timekeeping device used in Mechanical watches and some Clocks analogous to the Pendulum in a Pendulum clock. A watch is a timepiece that is made to be worn on a person The term now usually refers to a wristwatch, which is worn on the wrist with a strap or Bracelet. In Oceanography, a tidal Resonance occurs when the Tide excites one of the resonant modes of the ocean Tides Folklore in the Mi'kmaq First Nation claims that the tides in the Bay of Fundy are caused by a giant whale splashing in the water In Celestial mechanics, an orbital resonance occurs when two Orbiting bodies exert a regular periodic gravitational influence on each other usually due to their A natural satellite or moon is a Celestial body that Orbits a Planet or smaller body which is called the primary. The Solar System consists of the Sun and those celestial objects bound to it by Gravity. A gas giant (sometimes also known as a Jovian planet after the planet Jupiter, or giant planet) is a large Planet that is not primarily 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 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
• electrical resonance of tuned circuits in radios that allow individual stations to be picked up
• creation of coherent light by optical resonance in a "laser" cavity
• the shattering of crystal glasses when exposed to a musical tone of the right pitch (its resonance frequency). Electrical resonance occurs in an electric circuit at a particular resonance frequency when the impedance between the input and output of the An LC circuit is a variety of resonant circuit or tuned circuit and consists of an Inductor, represented by the letter L and a Capacitor, represented Radio is the transmission of signals by Modulation of electromagnetic waves with frequencies below those of visible Light. A laser is a device that emits Light ( Electromagnetic radiation) through a process called Stimulated emission. An optical cavity or optical resonator is an arrangement of Mirrors that forms a Standing wave Cavity resonator for Light waves Optical

Theory

For a linear oscillator with a resonance frequency Ω, the intensity of oscillations I when the system is driven with a driving frequency ω is given by:

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. The Cauchy–Lorentz distribution, named after Augustin Cauchy and Hendrik Lorentz, is a continuous Probability distribution. Γ is a parameter dependent on the damping of the oscillator, and is known as the linewidth of the resonance. This article is about the harmonic oscillator in classical mechanics Heavily damped oscillators tend to have broad linewidths, and respond to a wider range of driving frequencies around the resonance frequency. The linewidth is inversely proportional to the Q factor, which is a measure of the sharpness of the resonance. This article is about proportionality the mathematical relation For other uses of the terms Q and Q factor see Q value. In Physics and Engineering the quality

Resonators

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. In mechanics, degrees of freedom (DOF are the set of independent displacements and/or rotations that specify completely the displaced or deformed position and orientation This article is about the harmonic oscillator in classical mechanics Systems with one degree of freedom, such as a mass on a spring, pendulums, balance wheels, and LC tuned circuits have one resonance frequency. A pendulum is a mass that is attached to a pivot from which it can swing freely The balance wheel is the timekeeping device used in Mechanical watches and some Clocks analogous to the Pendulum in a Pendulum clock. An RLC circuit (also known as a Resonant circuit tuned circuit or LCR circuit is an Electrical circuit consisting of a Resistor (R an Systems with two degrees of freedom, such as coupled pendulums and resonant transformers can have two resonance frequencies. In Horology, a double pendulum is a system of two simple Pendulums on a common mounting which move in anti-phase A transformer is a device that transfers Electrical energy from one circuit to another through inductively coupled Electrical conductors 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 pipes, vibrating strings, quartz crystals, microwave cavities, and laser rods. A resonator is a device or system that exhibits Resonance or resonant behavior that is it naturally oscillates at some frequencies, called its resonance An organ pipe is a sound-producing element of the Pipe organ that resonates at a specific pitch when pressurized air (commonly referred to as wind A Vibration in a string is a Wave. Usually a vibrating string produces a Sound whose Frequency in most cases is constant Quartz (from German) is the most abundant Mineral in the Earth 's Continental crust (although Feldspar is more common in Microwaves are electromagnetic waves with Wavelengths ranging from 1 mm to 1 m or frequencies between 0 A laser is a device that emits Light ( Electromagnetic radiation) through a process called Stimulated emission. 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 frequency. A normal mode of an oscillating system is a pattern of motion in which all parts of the system move sinusoidally with the same frequency The fundamental tone, often referred to simply as the fundamental and abbreviated fo, is the lowest frequency in a harmonic series. The multiples are often called overtones. An overtone is a natural resonance or vibration frequency of a system There may be several such series of resonance frequencies, corresponding to different modes of vibration.

Old Tacoma Narrows bridge failure

Main article: Tacoma Narrows Bridge

The collapse of the Old Tacoma Narrows Bridge, nicknamed Galloping Gertie, in 1940 is sometimes characterized in physics textbooks as a classical example of resonance. The Tacoma Narrows Bridge is a pair of mile-long Suspension bridges in the U The Tacoma Narrows Bridge is a pair of mile-long Suspension bridges in the U This description is misleading, however. The catastrophic vibrations that destroyed the bridge were not due to simple mechanical resonance, but to a more complicated oscillation between the bridge and winds passing through it, known as aeroelastic flutter. Aeroelasticity is the science which studies the interaction among inertial, elastic, and aerodynamic forces Robert H. Scanlan, father of the field of bridge aerodynamics, wrote an article about this misunderstanding^[2].

Resonances in quantum mechanics

In quantum mechanics and quantum field theory resonances may appear in similar circumstances to classical physics. Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons In quantum field theory (QFT the forces between particles are mediated by other particles 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. Particle decay is the spontaneous process of one Elementary particle transforming into other elementary particles In that case, the formula just comes from the particle's propagator, with its mass replaced by the complex number M + iΓ. In 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 Complex plane In Mathematics, the complex numbers are an extension of the Real numbers obtained by adjoining an Imaginary unit, denoted The formula is further related to the particle's decay rate by the optical theorem. Particle decay is the spontaneous process of one Elementary particle transforming into other elementary particles In Physics, the optical theorem is a very general law of Wave Scattering theory, which relates the forward Scattering amplitude to the total

String resonance in music instruments

Main article: String resonance (music)

String resonance occurs on string instruments. String resonance occurs on String instruments. Strings or parts of strings may resonate at their Fundamental or Overtone frequencies when other strings String resonance occurs on String instruments. Strings or parts of strings may resonate at their Fundamental or Overtone frequencies when other strings A string instrument (or stringed instrument) is a Musical instrument that produces Sound by means of Vibrating strings In the Hornbostel-Sachs Strings or parts of strings may resonate at their fundamental or overtone frequencies when other strings are sounded. The fundamental tone, often referred to simply as the fundamental and abbreviated fo, is the lowest frequency in a harmonic series. An overtone is a natural resonance or vibration frequency of a system For example, an A string at 440 Hz will cause an E string at 330 Hz to resonate, because they share an overtone of 1320 Hz (the third overtone of A and fourth overtone of E).

See also

References

1. ^ Ogata, Katsuhiko. In Electrical engineering and Telecommunications, the center frequency of a filter or channel is a measure of a central frequency between the upper and lower This article is about the harmonic oscillator in classical mechanics A formant is a peak in the Frequency spectrum of a sound caused by acoustic Resonance. This article is about the harmonic oscillator in classical mechanics Electrical impedance, or simply impedance, describes a measure of opposition to a sinusoidal Alternating current (AC For other uses of the terms Q and Q factor see Q value. In Physics and Engineering the quality A resonator is a device or system that exhibits Resonance or resonant behavior that is it naturally oscillates at some frequencies, called its resonance Vibration refers to mechanical Oscillations about an equilibrium point. The Schumann resonances (SR are a set of spectrum peaks in the Extremely low frequency (ELF portion of the Earth 's Electromagnetic field spectrum Simple harmonic motion is the motion of a simple harmonic oscillator, a motion that is neither driven nor damped. An LC circuit is a variety of resonant circuit or tuned circuit and consists of an Inductor, represented by the letter L and a Capacitor, represented Electromagnetic radiation takes the form of self-propagating Waves in a Vacuum or in Matter. Sympathetic strings or resonance strings are auxiliary strings found on many Indian musical instruments as well as some Western Baroque instruments and a variety System Dynamics 4th Edition. University of Minnesota. 2004. (p. 617)
2. ^ K. Billah and R. Scanlan (1991), Resonance, Tacoma Narrows Bridge Failure, and Undergraduate Physics Textbooks, American Journal of Physics, 59(2), 118--124 (PDF)

External links

• Resonance - a chapter from an online textbook
• Greene, Brian, "Resonance in strings". The American Journal of Physics is a Peer-reviewed Scientific journal published by the American Association of Physics Teachers devoted to the educational Brian Greene (born February 9 1963 is a Theoretical physicist and one of the best-known string theorists. The Elegant Universe, NOVA (PBS)
• Hyperphysics section on resonance concepts
• A short FAQ on quantum resonances
• Resonance versus resonant (usage of terms)
• Wood and Air Resonance in a Harpsichord
• Java applet demonstrating resonances on a string when the frequency of the driving force is varied
• Breaking glass with sound, including high-speed footage of glass breaking