Text: http://en.wikipedia.org/wiki/Sympathetic_vibration Resonance can also mean: * Resonance (social) * Resonance (MIT) for an article about the group of a cappella singers. * Resonance (chemical) In physics, resonance is an increase in the oscillatory energy absorbed by a system when the frequency of the oscillations matches the system's natural frequency of vibration (its resonant frequency). Examples are the acoustic resonances of musical instruments, the tidal resonance of the Bay of Fundy, orbital resonance as exemplified by some of the Jovian moons, the resonance of the basilar membrane in the biological transduction of auditory input, and resonance in electronic circuits. A resonant object, whether mechanical, acoustic, or electromagnetic, 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 Table of contents [showhide] 1 Mechanics 2 Electronic circuits 3 Music 4 Theory 5 See also 6 External links [edit] Mechanics A swing set is a simple example of a resonant system that most people have practical experience with. It is a form of pendulum, a type of resonant system. If you excite the system (push the swing) with a period between pushes equal to the inverse of the pendulum's natural frequency, the swing will swing higher and higher, but if you excite it at a different frequency, it will be very difficult. The resonant frequency of a pendulum is related to the equation f = {1 \over 2 \pi} \sqrt {g \over L} where g is the gravitational constant (9.8 m/s2 for Earth), and L is the length from the pivot point to the center of mass. Note that the frequency does not depend on mass. A swing cannot easily be excited by harmonic frequencies, but can be excited by subharmonics. An improperly constructed bridge, like the Tacoma Narrows Bridge (nicknamed Galloping Gertie), can be destroyed by its resonance; that is why soldiers are trained not to march in lockstep across a bridge, but rather in breakstep. [edit] Electronic circuits 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. Resonance occurs because the collapsing magnetic field of the inductor generates an electric current in its windings that charges the capacitor and the discharging capacitor provides an electric current that builds the magnetic field in the inductor, and the process is repeated. An analogy is a mechanical pendulum. At resonance, the series impedance of the two elements is at a minimum and the parallel impedance is a maximum. Resonance is used for tuning and filtering, because resonance occurs at a particular frequency for given values of inductance and capacitance. Resonance can be detrimental to the operation of communications circuits by causing unwanted sustained and transient oscillations that may cause noise, signal distortion, and damage to circuit elements. Since the inductive reactance and the capacitive reactance are of equal magnitude, ?L = 1/?C , where ? = 2¼f , in which f is the resonant frequency in hertz, L is the inductance in henries, and C is the capacitance in farads when standard SI units are used. Source: Federal Standard 1037C [edit] Music Resonance is an important consideration for instrument builders as most acoustic instruments utilize resonators, such as the strings and body of a violin, the length of tube in a flute, and the shape of a drum membrane. Violin (or harp, guitar, piano, etc.) strings have a fundamental resonant frequency directly related to the length and tension of the string. The wavelength that will create the first resonance on the string is equal to twice the length of the string. This frequency is related to the speed v of a wave traveling down the string by the equation f = {v \over 2L} where L is the length of the string (for a string fixed at both ends). The speed of a wave through a string or wire is related to its tension T and the mass per unit length ?: v = \sqrt {T \over \rho} So the frequency is related to the properties of the string by the equation f = {\sqrt {T \over \rho} \over 2 L} = {\sqrt {T \over m / L} \over 2 L} where T is the tension, ? is the mass per unit length, and m is the total mass. Higher tension and shorter lengths increase the resonant frequency, and vice versa. The string also has a resonance at integer multiples of the fundamental frequency f. It will then also resonate at 2f, 3f, 4f, and so on. When the string is excited with an impulsive function (a finger pluck or a strike by a hammer), the string vibrates at all the frequencies present in the impulse (an impulsive function theoretically contains 'all' frequencies). Those frequencies that are not one of the resonances are quickly filtered out - they are attenuated - and all that is left is the harmonic vibrations that we hear as a musical note. The resonance of a tube of air is related to the length of the tube and whether it has closed or open ends. When a wave reaches the end of the tube, part of it will be reflected back into the tube, and part will be transmitted to the outside air. An open end will reflect a wave with no inversion; in other words, a compression wave will be reflected as a compression wave. A closed end will invert the wave that is reflected; in other words, a compression wave will be reflected as a rarefaction wave. Examples of instruments that have both ends open are flute, saxophone, oboe, and trombone. An example of an instrument that has one closed end and one open end is a clarinet. Vibrating air columns also have resonances at harmonics, like strings. Tubes with both ends open resonate at the frequency f = {v \over 2L} This is similar to the string formula, except v now becomes the speed of sound in air. A tube with one end closed will have a resonance of f = {v \over 4L} This type of tube can only produce odd harmonics, f, 3f, 5f, and so on. Composers have begun to make resonance the subject of compositions. Alvin Lucier has used acoustic instruments and sine wave generators to explore the resonance of objects large and small in many of his compositions. The complex inharmonic partials of a swell shaped crescendo and decrescendo on a tam tam or other percussion instrument interact with room resonances in James Tenney's Koan: Having Never Written A Note For Percussion. Pauline Oliveros and Stuart Dempster regularly perform in large reverberant spaces such as the two million gallon cistern at Fort Warden, WA, which has a reverb with a 45 second decay. [edit] Theory For an oscillator with a resonant frequency ?, the amplitude of oscillation A when the system is driven with a driving frequency ? is given by: A(\omega) \; \alpha \; \frac{\frac{\Gamma}{2}}{(\omega - \Omega)^2 + \left( \frac{\Gamma}{2} \right)^2 }. This is a Lorentzian function, and this response is found in many physical situations involving resonant systems. ? is a parameter dependent on the damping of the oscillator, and is known as the linewidth of the resonance. Strongly damped oscillators tend to have narrower linewidths, and respond to a narrower range of driving frequencies around the resonant frequency. [edit] See also * Orbital resonance, Tidal locking, Tidal resonance, RLC series circuit, wave, Q factor, Impedance, acoustics, Harmony, Antenna theory, Music theory, Schumann resonance, Cavity resonator, Basilar membrane, Center frequency

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