- This article is about resonance in physics. For other senses of this term, see resonance (disambiguation).
In physics, resonance is the tendency of a system to absorb more energy when the frequency of the oscillations matches the system's natural frequency of vibration (its resonant frequency) than it does at other frequencies. Examples are the acoustic resonances of musical instruments, 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 proton nuclear magnetic resonance in the biological bio resonance transduction of auditory input, and resonance in electronic circuits.
A resonant object, whether mechanical, acoustic, or electromagnetic, will probably have more than one resonant frequency (especially harmonics of the strongest resonance frequency mechanical resonance frequency resonance). It will be easy to vibrate at those frequencies, and more difficult to vibrate at other frequencies. It will "pick out" its resonant frequency from a complex excitation, such as an impulse or a wideband noise excitation. phased array resonance In effect, it is filtering out all frequencies other than its resonance.
See also: center frequency
Mechanics
A swing set is a simple example of a resonant system that most people have practical experience with. It is a form of pendulum, a type of resonant system. If you excite the system (push the swing) with a period between pushes equal to nuclear magnetic resonance spectroscopy the resonance mobile electronics inverse of the pendulum's natural frequency, the swing will swing higher and higher, but if you excite it at a different frequency, it roper resonance will be very difficult. The resonant frequency of a pendulum, the only frequency at which ground magnetic resonance imaging in breast cancer resonance it will vibrate, is given approximately, for small displacements, by the equation
- steel column resonance
where g is the acceleration due to gravity (9.8 m/s2 for Earth), and L lindsays beethoven resonance is the length from the pivot point to the center of mass. (An elliptic integral yields a description for any displacement.) harmonic resonance Note that, in this approximation, the frequency dislodged resonance does not depend on mass. A swing cannot easily be excited by harmonic frequencies, but can be excited by subharmonics.
Resonance may cause violent swaying motions in improperly constructed nuclear magnetic resonance bridges. Both the Tacoma Narrows Bridge (nicknamed Galloping Gertie) and the London Millennium Footbridge (nicknamed the Wobbly Bridge) exhibited this problem. A bridge can even be destroyed resonance structure of cyclopentanone by its resonance; that is why soldiers are trained not to march in lockstep across a bridge, but rather in breakstep.
Mechanical resonators work by transferring energy repeatedly from kinetic to potential form and back again. resonance vibration In the pendulum, for example, all the energy is stored as gravitational energy (a form of potential energy) when the bob magnetic resonance angiogram is instantaneously motionless bio resonance therapy at the top of its swing. This energy is proportional to both the mass of the bob and its height above the resonance leedskalnin lowest point. As the bob descends and picks up speed, its potential energy is gradually converted to kinetic energy (energy of movement), which is proportional to the bob's mass and to the square of its speed. When the bob is at the bottom of its travel, it has maximum kinetic energy and minimum potential energy. The same process then happens in reverse as the bob climbs towards the top of its swing.
Other mechanical systems store potential energy in different forms. For example, a spring/mass system stores energy as tension in the spring, which is ultimately stored as the energy of bonds between atoms.
Electronic circuits
In an electrical circuit, resonance occurs at a particular frequency when the inductive reactance and the capacitive reactance are of equal magnitude, causing electrical energy to oscillate between the magnetic field of the inductor and the electric field of the capacitor.
Resonance occurs because the collapsing magnetic field of the inductor generates an electric current in its phonon resonance transmutation windings that charges the capacitor and the discharging capacitor provides magnetic resonance spectroscopy an electric current that builds subsynchronous resonance the magnetic field in the inductor, and the process is schuman resonance repeated. An analogy is a mechanical pendulum.
At resonance structures of butyraldehyde resonance, resonance energy methods the series impedance electron spin resonance of the two elements is at a minimum and the parallel impedance is a maximum. Resonance is used for tuning and filtering, because resonance occurs at a particular frequency for given values of inductance and capacitance. Resonance can be detrimental to the operation of communications schumann resonance circuits by causing unwanted sustained and transient oscillations that may cause noise, signal distortion, and damage to circuit elements.
Since the inductive reactance and the capacitive morphic resonance reactance are of equal magnitude, ωL = 1/ωC, where ω = 2πf, in which f is the cyclopentanone resonance structures resonant frequency in hertz, L is the inductance in henries, and C is the capacitance in farads when standard SI units are magnetic resonance imaging used.
- Source: Federal Standard 1037C
Acoustics
Resonance is an important consideration for instrument builders as most acoustic instruments use resonators, such as the strings and body of a violin, the length of tube in a flute, and the shape of a drum membrane.
- Resonance of a string.
Lute (harp, guitar, piano, surface plasmon resonance violin etc.) strings have a fundamental resonant frequency directly related to the length and tension of the string. The wavelength that will create the first resonance on the string is equal to twice the length of the string. This frequency is related to the speed v of a wave traveling down the string by the equation
where L is the length of the string (for a string fixed at both ends). The speed of a wave through a string or magnetic resonance angiography wire is related to its tension T and the mass per unit length ρ:
So the frequency is related to the properties of the string by bass reflex column resonance the equation
where T is the tension, ρ is the mass per unit length, and m is the total mass.
Higher tension and shorter lengths increase the resonant frequency, and vice definition of resonance versa. The string also has a resonance at integer multiples of the fundamental frequency f. It will then resonance structures also resonate at 2f, 3f, 4f, and so on. When the string is excited with an impulsive function (a finger pluck or a strike by a hammer), the string vibrates at all the frequencies present in the impulse (an impulsive function theoretically contains 'all' frequencies). Those frequencies that are not one of the resonances are quickly filtered out—they are attenuated—and all that is left is the harmonic vibrations that we hear as a musical note.
- Resonance of a tube of air.
The resonance of a tube of air is related to the length of the tube and whether it has closed or open ends. When a wave reaches the end of the tube, part of it will be reflected back into the tube, and sympathetic resonance technology-side effects part will be transmitted to the outside air. An open end will reflect magnetic resonance imaging crime solved a wave with no inversion; in other words, a compression wave will be reflected as a compression wave. A closed end will invert the wave that is reflected; in other words, a compression self resonance wave will be reflected as a rarefaction wave. Examples of instruments that have both ends open are the flute, saxophone, oboe, and trombone. An example of an instrument that has one closed end and one open end is the clarinet. Vibrating air columns also have resonances at harmonics, like strings. Tubes with resonance both ends open resonate at the frequency
This is similar to the string formula, except v now becomes the speed of sound in air (which is approximately 340 meters per second at 20 °C and at sea level).
Note however that in practise the exact point at which a sound wave is reflecting at an open end is not perfectly at the end section of the tube. The wave in fact progresses over a small distance outside the tube and the reflection ratio mechanical resonance is also not perfectly equal to one. This phenomena is caused by the fact that the open end does not behave like creating resonance when you sing an infinite acoustical impedance. It has a finite value, called radiation impedance, which is dependent on the diameter of the tube, the wavelength and the type of reflection board possibly present around the opening structural resonance agitator of the tube.
A tube with one end closed will have a resonance of
This type of tube can only produce odd harmonics, f, 3f, 5f, and so on.
Composers have begun to make resonance the subject of compositions. Alvin Lucier has used acoustic instruments and sine wave generators to explore the resonance of objects large and small in many of his compositions. The complex inharmonic partials of a swell shaped crescendo and decrescendo on a tam tam or other percussion instrument interact with room resonances in James Tenney's Koan: Having Never Written A Note For Percussion. Pauline Oliveros and Stuart Dempster regularly perform in large reverberant spaces such as magnetic resonance imaging of the shoulder gentili the two million gallon cistern at Fort Warden, WA, which has a reverb with a 45 second decay.
Theory
For an oscillator with a resonant 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, earth resonance receivers and this response is found in many physical situations involving resonant systems. Γ is a parameter dependent on the damping 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 to the Q factor, which is a measure of the sharpness of the resonance.
Quantum mechanics
A resonance is a quantum state whose mean energy lies above the fragmentation threshold of a system and is associated with:
- a pronounced variation of the cross sections if the fragmentation energy lies in the neighbourhood of the energy of the resonance (energy-dependent definition) - The width of this neighbourhood is called the width of the resonance.
- an exponential decay of the system when the system has a mean energy close to the resonance energy (time-dependent definition, i.e. in time-resolved spectroscopy) - The lifetime (or inverse of the exponent of the exponential signal) of the resonance is proportional to the inverse of its width. Resonances are usually classified into shape and Feshbach resonances or into Breit-Wigner and Fano resonances.
Quantum field theory
In quantum field theory, resonance is an unstable particle/bound state. It is characterized by a complex pole off the real line in the S-matrix (which happens to be analytic). A sharp resonance is a resonance with a sharp peak in the S-matrix (which corresponds to a long lifetime compared to the reciprocal of its mass) while a broad resonance is electron paramagnetic resonance of fullerenes a resonance with a spread out peak (which corresponds magnetic resonance imaging mri to a short lifetime relative to the reciprocal of its mass). If a resonance is too broad, it might not be considered as a particle at all even if it has a complex pole (far magnetic resonance from the real line).
See also relativistic Breit-Wigner distribution
If the resonance happens to be a "fundamental particle" (i.e. described by a "fundamental field" of its own), it shows up as a complex pole off the real line in the 2-point connected correlation function (i.e. the propagator).
See also
- Acoustics
- Antenna theory
- Basilar membrane
- Cavity resonator
- Center frequency
- Formant
- Harmonic oscillator
- Harmony
- Impedance
- Music theory
- Orbital resonance
- Q factor
- Resonator
- RLC circuit
- Schumann resonance
- Simple harmonic motion
- Tidal locking
- Tidal resonance
- Wave
- Gluonic vacuum field
External links
- RMCybernetics - Resonance Resonance Research.
- Greene, Brian, "Resonance in strings". The Elegant Universe, magnetic resonance imaging equipment NOVA (PBS)
- Hyperphysics section on resonance concepts
- A short FAQ on quantum resonances
- Resonance versus resonant
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Electronics Topics
The field of electronics is the study and use of systems that operate by controlling the flow of electrons or other electrically charged particles in devices such as thermionic valves and semiconductors. The design and construction of electronic circuits to solve practical problems is part of the fields of electronic engineering, and the hardware design side of computer engineering. The study of new semiconductor devices and their technology is sometimes considered as a branch of physics.
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