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Encyclopedia > Resonance

## Contents

In physics, resonance is the tendency of a system to oscillate at maximum amplitude at a certain frequency. This frequency is known as the system's natural frequency of vibration, resonant frequency, or eigenfrequency. Physics (from the Greek, (phÃºsis), nature and (phusikÃ©), knowledge of nature) is the science concerned with the discovery and understanding of the fundamental laws which govern matter, energy, space, and time. ... Amplitude is a nonnegative scalar measure of a waves magnitude of oscillation, that is, magnitude of the maximum disturbance in the medium during one wave cycle. ... Sine waves of various frequencies; the bottom waves have higher frequencies than those above. ... Look up vibration in Wiktionary, the free dictionary. ...

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 in the biological transduction of auditory input, resonance in electrical circuits and the shattering of crystal glasses when exposed to an acoustic note of appropriate pitch and strength. Acoustic 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. ... A musical instrument is a device that has been constructed or modified with the purpose of making music. ... In oceanography, tidal resonance is a phenomenon perhaps best exemplified in the Bay of Fundy. ... The Bay of Fundy (French: ) is a bay located 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. ... In celestial mechanics, an orbital resonance occurs when two orbiting bodies exert a regular, periodic gravitational influence on each other. ... Moons of the Solar System scaled to Earths Moon A natural satellite is an object that orbits a planet or other body larger than itself and which is not man-made. ... Major features of the Solar System (not to scale, from left to right): Pluto, Neptune, Uranus, Saturn, Jupiter, the asteroid belt, the Sun, Mercury, Venus, Earth & Moon, and Mars. ... A gas giant is a large planet that is not composed mostly of rock or other solid matter. ... Cross section of the cochlea. ... The word transduction has several meanings: In developmental psychology, transduction is reasoning from specific cases to specific cases, typically employed by children. ... 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. ...

A resonant object, whether mechanical, acoustic, or electrical, will probably have more than one resonance frequency (especially harmonics of the strongest resonance). It will be easy to vibrate at those frequencies, and more difficult to vibrate at other frequencies. It will "pick out" its resonance frequency from a complex excitation, such as an impulse or a wideband noise excitation. In effect, it is filtering out all frequencies other than its resonance. A swing set is a simple example of a resonant system that most people have practical experience with. ...

See also: center frequency The frequency axis of this symbolic diagram would be logarithmically scaled. ...

## Theory

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

$I(omega) propto frac{frac{Gamma}{2}}{(omega - Omega)^2 + left( frac{Gamma}{2} right)^2 }.$

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 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. ... In classical mechanics, a Harmonic oscillator is a system which, when displaced from its equilibrium position, experiences a restoring force proportional to the displacement according to Hookes law: where is a positive constant. ... The Q factor or quality factor is a measure of the rate at which a vibrating system dissipates its energy into heat. ...

## 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.

In nuclear and particle physics, the concept of a cross section is used to express the likelihood of interaction between particles. ... In physics and physical chemistry, time-resolved spectroscopy is the study of dynamical processes in materials or chemical compounds by means of spectroscopic techniques. ... In quantum mechanics, in contrast with a Feshbach resonance, a shape resonance is a resonance which is not turned into a bound state if the coupling between some degrees of freedom and the degrees of freedom associated to the fragmentation (reaction coordinates) were set to zero. ... In quantum mechanics, a Feshbach resonance, in contrast to a shape resonance, is a resonance of a system with more than one degree of freedom, which would turn into a bound state if the coupling between some degrees of freedom and the degrees of freedom associated to the fragmentation (reaction... The Cauchy-Lorentz distribution, named after Augustin Cauchy, is a continuous probability distribution with probability density function where x0 is the location parameter, specifying the location of the peak of the distribution, and Î³ is the scale parameter which specifies the half-width at half-maximum (HWHM). ... A Fano resonance, in contrast with a Breit-Wigner resonance, is a resonance which corresponding profile in the cross-secction has the so-called Fano shape, i. ...

## Quantum field theory

In quantum field theory, most particles are unstable particles, i.e., they decay into sets of lighter particles. If the decay is fast, the mass of the particle is not sharply defined. The mass is undefined and ruled sophisticated. Such particles are usually called resonances. Typical of a resonance is the decay into a continuum of states, i.e., the center-of-mass energy of the decay products, or daughter particles, vary. The energy dependence of such a resonance is described by the relativistic Breit-Wigner distribution, in the simplest case. In this case the "driving frequency" corresponds to the energy with which the resonance is produced, the "resonant frequency" corresponds to the unstable particle's mass, and the linewidth Γ of the resonance corresponds to the inverse of the lifetime τ of the particle, Γ = 1 / τ. Quantum field theory (QFT) is the application of quantum mechanics to fields. ... A quantity is said to be subject to exponential decay if it decreases at a rate proportional to its value. ... NB: The information in this article should be reviewed. ...

## 'Old Tacoma Narrows' bridge failure

The Old Tacoma Narrows Bridge has been popularized in physics textbooks as a classical example of resonance, but this description is misleading. It is more correct to say that it failed due to the action of self-excited forces, by an aeroelastic phenomenon known as flutter. Robert H. Scanlan, father of the field of bridge aerodynamics, wrote an article about this misunderstanding[1]. The Tacoma Narrows Bridge is a mile-long (1600 meter) suspension bridge with a main span of 2800 feet (850 m) (the third-largest in the world when it was first built[1]) that carries Washington State Route 16 across the Tacoma Narrows of Puget Sound from Tacoma to Gig... Aeroelasticity is the science which studies the interaction among inertial, elastic, and aerodynamic forces. ... Flutter: In electronics, rapid variation of signal parameters, such as amplitude, phase, and frequency. ...

The frequency axis of this symbolic diagram would be logarithmically scaled. ... A Harmonic oscillator is a system which, when displaced from its equilibrium position, experiences a restoring force proportional to the displacement : where is a positive constant. ... Spectrogram of American English vowels [i, u, É‘] showing the formants f1 and f2 A formant is a peak in an acoustic frequency spectrum which results from the resonant frequencies of any acoustical system. ... In classical mechanics, a Harmonic oscillator is a system which, when displaced from its equilibrium position, experiences a restoring force proportional to the displacement according to Hookes law: where is a positive constant. ... Electrical impedance, or simply impedance, is a measure of opposition to a sinusoidal alternating electric current. ... The Q factor or quality factor is a measure of the rate at which a vibrating system dissipates its energy into heat. ... A resonator is a device or part that vibrates (or oscillates) with waves. ... Look up vibration in Wiktionary, the free dictionary. ... The Schumann Resonance is a set of spectrum peaks in the ELF portion of the Earths electromagnetic field spectrum. ... Simple harmonic motion is the motion of a simple harmonic oscillator, a motion that is neither driven nor damped. ... An RLC circuit (sometimes known as resonant or tuned circuit) is an electrical circuit comprising a resistor (R), an inductor (L), and a capacitor (C), connected in series or in parallel. ... Electromagnetic radiation is a propagating wave in space with electric and magnetic components. ... Sympathetic strings are strings on musical instruments which begin resonating, not due to any external influence such as picking or bowing, but due to another note (or frequency). ...

## Reference

1. ^ K. Billah and R. Scanlan (1991), Resonance, Tacoma Narrows Bridge Failure, and Undergraduate Physics Textbooks, American Journal of Physics, 59(2), 118--124 (PDF)

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