resonance - Examples, Theory, Quantum mechanics, 'Old Tacoma Narrows' bridge failure

A condition obtained when the frequency of the force driving an oscillating system matches a natural frequency of the system. It is characterized by especially large amplitudes of oscillation at these specific frequencies.

In physics, resonance is the tendency of a system to oscillate with high amplitude when excited by energy at a certain frequency.

Examples

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.

A resonant object, whether mechanical, acoustic, or electrical, will probably have more than one resonant frequency (especially harmonics of the strongest resonance).

See also: center frequency

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:

The intensity is defined as the square of the amplitude of the oscillations.

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. Resonances are usually classified into shape and Feshbach resonances or into Breit-Wigner and Fano 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.

'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.