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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: there is mechanical resonance, acoustic resonance, electromagnetic resonance, and resonance of 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.

Resonance was discovered by Galileo Galilei with his investigations of pendulums beginning in 1602.

Resonance occurs widely in nature, and is exploited in many man-made devices. It is the mechanism by which virtually all sinusoidal waves and vibrations are generated. 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 human vocal cords
- the timekeeping mechanisms of all modern clocks and watches: the balance wheel in a mechanical watch and the quartz crystal in a quartz 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.
- AM radios use resonant coil pickups on ferrite rods as compact aerials (much smaller than the wavelength)
- electrical resonance of tuned circuits in radios and TVs that allow individual stations to be picked up
- creation of coherent light by optical resonance in a "laser" cavity
- the shattering of a crystal wineglass when exposed to a musical tone of the right pitch (its resonance frequency).

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

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 resonance frequency. The linewidth is inversely proportional to the Q factor, which is a measure of the sharpness of the resonance.

A physical system can have as many resonance frequencies as it has degrees of freedom; each degree of freedom can vibrate as a harmonic oscillator. Systems with one degree of freedom, such as a mass on a spring, pendulums, balance wheels, and LC tuned circuits have one resonance frequency. Systems with two degrees of freedom, such as coupled pendulums and resonant transformers can have two resonance frequencies. As the number of coupled harmonic oscillators grows, the time it takes to transfer energy from one to the next becomes significant. The vibrations in them begin to travel through the coupled harmonic oscillators in waves, from one oscillator to the next.

Extended objects that experience resonance due to vibrations inside them are called resonators, such as organ pipes, vibrating strings, quartz crystals, microwave cavities, and laser rods. Since these can be viewed as being made of millions of coupled moving parts (such as atoms), they can have millions of resonance frequencies. The vibrations inside them travel as waves, at an approximately constant velocity, bouncing back and forth between the sides of the resonator. If the distance between the sides is $d,$, the length of a round trip is $2d,$. In order to cause resonance, the phase of a sinusoidal wave after a round trip has to be equal to the initial phase, so the waves will reinforce. So the condition for resonance in a resonator is that the round trip distance, $2d,$, be equal to an integral number of wavelengths $lambda,$ of the wave:

- $2d\; =\; Nlambda,qquadqquad\; N\; in\; \{1,2,3...\}$

If the velocity of a wave is $v,$, the frequency is $f\; =\; v\; /\; lambda,$ so the resonance frequencies are:

- $f\; =\; frac\{Nv\}\{2d\}qquadqquad\; N\; in\; \{1,2,3...\}$

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 resonance frequencies, corresponding to different modes of vibration.

- Resonance - a chapter from an online textbook
- Greene, Brian, " Resonance in strings". The Elegant Universe, NOVA (PBS)
- Hyperphysics section on resonance concepts
- A short FAQ on quantum resonances
- Resonance versus resonant (usage of terms)
- Wood and Air Resonance in a Harpsichord
- Java applet demonstrating resonances on a string when the frequency of the driving force is varied
- Breaking glass with sound, including high-speed footage of glass breaking

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Last updated on Friday October 03, 2008 at 02:48:39 PDT (GMT -0700)

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This article is licensed under the GNU Free Documentation License.

Last updated on Friday October 03, 2008 at 02:48:39 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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