Resonance Totally Explained

Everything about Resonance totally explained

ť 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 oscillate at maximum amplitude at certain frequencies, known as the system's resonance frequencies (or resonant frequencies). At these frequencies, even small periodic driving forces can produce large amplitude vibrations, because the system stores vibrational energy. When damping is small, the resonance frequency is approximately equal to the natural frequency of the system, which is the frequency of free vibrations. Resonant phenomena occur with all type of vibrations or waves; mechanical (acoustic), electromagnetic, and quantum wave functions. Resonant systems can be used to generate vibrations of a specific frequency, or pick out specific frequencies from a complex vibration containing many frequencies.

Examples

One familiar example is a playground swing, which acts as a pendulum. 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 at the resonance frequency, while some of this energy is canceled out by the inertial energy of the swing when they're not.
Resonance occurs widely in nature, and is exploited in many man-made devices. 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. 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.
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).

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:
ť

I(omega) propto frac

So the resonance frequencies of resonators, called normal modes, are equally spaced multiples of a lowest frequency called the fundamental frequency. The multiples are often called overtones. There may be several such series of resonant frequencies, corresponding to different modes of vibration.

Old Tacoma Narrows bridge failure

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. 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. Robert H. Scanlan, father of the field of bridge aerodynamics, wrote an article about this misunderstanding.

Resonances in quantum mechanics

In quantum mechanics and quantum field theory resonances may appear in similar circumstances to classical physics. However, they can also be thought of as unstable particles, with the formula above still valid if the

Gamma

is the decay rate and

Omega

replaced by the particle's mass M. In that case, the formula just comes from the particle's propagator, with its mass replaced by the complex number

M+iGamma

. The formula is further related to the particle's decay rate by the optical theorem.

String resonance in music instruments

String resonance occurs on string instruments. Strings or parts of strings may resonate at their fundamental or overtone frequencies when other strings are sounded. 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).

Further Information

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