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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 resonant frequency. When damping is small, the resonant frequency is approximately equal to the natural frequency of the system, which is the frequency of free vibrations.
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 a strong enough sound that causes the glass to resonate.
A resonant object, whether mechanical, acoustic, or electrical, will probably have more than one resonant 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 resonant 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.
See also: center frequency
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. 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.
The collapse of the Old Tacoma Narrows Bridge in 1940 has been characterized 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 a phenomenon known as aeroelastic flutter. Robert H. Scanlan, father of the field of bridge aerodynamics, wrote an article about this misunderstanding[1].