Resonance K-12 Experiments
In physics, resonance is the phenomenon of producing large amplitude of vibrations by a small periodic driving force. It is the tendency of a system to oscillate at maximum amplitude at a certain frequency. This frequency is known as the system's resonance frequency (or resonant frequency). When damping is small, the resonance frequency is approximately equal to the natural frequency of the system, which is the frequency of free vibrations. Under resonance condition the energy supplied by the driving force is sufficient enough to overcome friction. ExamplesOne familiar example is a playground swing, which is a crude pendulum. When pushing someone in a swing, pushes that are timed with the correct interval between them (the resonant frequency), will make the swing go higher and higher (maximum amplitude), while attempting to push the swing at a faster or slower rate will result in much smaller arcs. Resonance occurs in nature, and is exploited in many man-made devices. Some examples:
A resonator, whether mechanical, acoustic, or electrical, will probably have more than one resonance 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 resonance 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 TheoryFor 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: 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. Old Tacoma Narrows bridge failureThe 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. It would be more correct to say that the bridge failed due to the action of self-excited forces upon it, largely through a phenomenon known as aeroelastic flutter. Robert H. Scanlan, father of the field of bridge aerodynamics, wrote an article about this misunderstanding[1]. Cause of collapseThe bridge was solidly built, with girders of carbon steel anchored in huge blocks of concrete. Preceding designs typically had open lattice beam trusses underneath the roadbed. This bridge was the first of its type to employ plate girders (pairs of deep I beams) to support the roadbed. With the earlier designs any wind would simply pass through the truss, but in the new design the wind would be diverted above and below the structure. Shortly after construction finished at the end of June (opened to traffic on July 1, 1940), it was discovered that the bridge would sway and buckle dangerously in relatively mild windy conditions for the area. This resonance was transverse, meaning the bridge buckled along its length, with the roadbed alternately raised and depressed in certain locations -- one half of the central span would rise while the other lowered. Drivers would see cars approaching from the other direction disappear into valleys which were dynamically appearing and disappearing. From this behavior, a local humorist coined the nickname "Galloping Gertie". However, the mass of the bridge was considered sufficient to keep it structurally sound. The failure of the bridge occurred when a never-before-seen twisting mode occurred, from winds at a mild 40 MPH. This is called a torsional, rather than longitudinal, mode (see also torque) whereby when the left side of the roadway went down, the right side would rise, and vice-versa, with the centerline of the road remaining still. Specifically, it was the second torsional mode, in which the midpoint of the bridge remained motionless while the two halves of the bridge twisted in opposite directions. Two men proved this point by walking along the center line, unaffected by the flapping of the roadway rising and falling to each side. This vibration was due to aeroelastic flutter. Flutter occurs when a torsional disturbance in the structure increases the angle of attack of the bridge (that is, the angle between the wind and the bridge). The structure responds by twisting further. Eventually, the angle of attack increases to the point of stall, and the bridge begins to twist in the opposite direction. In the case of the Tacoma Narrows Bridge, this mode was negatively damped (or had positive feedback), meaning it increased in amplitude with each cycle because the wind pumped in more energy than the flexing of the structure dissipated. Eventually, the amplitude of the motion increased beyond the strength of a vital part, in this case the suspender cables. Once several cables failed, the weight of the deck transferred to the adjacent cables which broke in turn until almost all of the central deck fell into the water below the span. The bridge's spectacular self-destruction is often used as an object lesson in the necessity to consider both aerodynamics and resonance effects in civil and structural engineering. However the effect that caused the destruction of the bridge should not be confused with forced resonance (as from the periodic motion induced by a group of soldiers marching in step across a bridge).[8] In the case of the Tacoma Narrows Bridge, there was no periodic disturbance. The wind was steady at 42 mph (67 km/h). The frequency of the destructive mode, 0.2 Hz, was neither a natural mode of the isolated structure nor the frequency of blunt-body vortex shedding of the bridge at that wind speed. The event can only be understood while considering the coupled aerodynamic and structural system which requires rigorous mathematical analysis to reveal all the degrees of freedom of the particular structure and the set of design loads imposed. In 1943, New York City's similarly slim Whitestone Bridge was retrofitted with a 14-foot deep Warren truss and Diagonal stays to reduce deck oscillations. The Warren Truss was removed in 2001 and replaced with hydraulic dampers and deck-edge fairings to maintain stability. Resonances in quantum mechanicsIn 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 Γ is the decay rate and Ω 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 + iΓ. The formula is further related to the particle's decay rate by the optical theorem.
String resonance in music instrumentsString 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). See also
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Mechanical resonance is the tendency of a mechanical system to absorb more energy when the frequency of its oscillations matches the system's natural frequency of vibration (its resonance frequency or resonant frequency) than it does at other frequencies.
DescriptionA swing set is a simple example of a resonant system that most people have practical experience with. It is a form of pendulum. If the system is excited (pushed) with a period between pushes equal to the inverse of the pendulum's natural frequency, the swing will swing higher and higher, but if excited it at a different frequency, it will be difficult to move. The resonance frequency of a pendulum, the only frequency at which it will vibrate, is given approximately, for small displacements, by the equation[1]: where g is the acceleration due to gravity (about 9.8 m/s2 near the surface of Earth), and L is the length from the pivot point to the center of mass. (An elliptic integral yields a description for any displacement.) Note that, in this approximation, the frequency does not depend on mass. Mechanical resonators work by transferring energy repeatedly from kinetic to potential form and back again. In the pendulum, for example, all the energy is stored as gravitational energy (a form of potential energy) when the bob is instantaneously motionless at the top of its swing. This energy is proportional to both the mass of the bob and its height above the lowest point. As the bob descends and picks up speed, its potential energy is gradually converted to kinetic energy (energy of movement), which is proportional to the bob's mass and to the square of its speed. When the bob is at the bottom of its travel, it has maximum kinetic energy and minimum potential energy. The same process then happens in reverse as the bob climbs towards the top of its swing. Some resonant objects have more than one resonance frequency, particularly at harmonics (multiples) of the strongest resonance. It will vibrate easily at those frequencies, and less so at other frequencies. It will "pick out" its resonance 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. In the example above, the swing cannot easily be excited by harmonic frequencies, but can be excited by subharmonics. ExamplesVarious examples of mechanical resonance include:
Resonance may cause violent swaying motions in improperly constructed structures, such as bridges and buildings. Both the Old Tacoma Narrows Bridge (nicknamed Galloping Gertie) and the London Millennium Footbridge (nicknamed the Wobbly Bridge) exhibited this problem. A faulty bridge can even be destroyed by its resonance (see "Angers Bridge"; that is why soldiers are trained not to march in lockstep across a bridge, although it is suspected to be a myth, see eg., MythBusters (season 2). Mechanical systems store potential energy in different forms. For example, a spring/mass system stores energy as tension in the spring, which is ultimately stored as the energy of bonds between atoms. ApplicationsVarious method of inducing mechanical resonance in a medium exist. Mechanical waves can be generated in a medium by subjecting an electromechanical element to an alternating electric field having a frequency which induces mechanical resonance and is below any electrical resonance frequency.[2] Such devices can apply mechanical energy from an external source to an element to mechanically stress the element or apply mechanical energy produced by the element to an external load. The United States Patent Office classifies devices that tests mechanical resonance under subclass 579, resonance, frequency, or amplitude study, of Class 73, Measuring and testing. This subclass is itself indented under subclass 570, Vibration.[3] Such devices test an article or mechanism by subjecting it to a vibratory force for determining qualities, characteristics, or conditions thereof, or sensing, studying or making analysis of the vibrations otherwise generated in or existing in the article or mechanism. Devices include methods to cause vibrations at a natural mechanical resonance and measure the frequency and/or amplitude the resonance made. Various devices study the amplitude response over a frequency range is made. This includes nodal points, wave lengths, and standing wave characteristics measured under predetermined vibration conditions. Earthquake machine
Nikola Tesla established a laboratory on Houston Street in New York at 46 E. There, at one point while experimenting with mechanical oscillators, he allegedly generated a resonance of several buildings causing complaints to the police. As the speed grew he hit the resonance frequency of his own building and belatedly realizing the danger he was forced to apply a sledge hammer to terminate the experiment, just as the astonished police arrived.[4] The Discovery Channel's popular MythBusters show debunked Tesla's claim that he had created an "Earthquake Machine" in their 60th episode. They tested the physical phenomenon known as mechanical resonance on a traffic bridge, which today are built to withstand such forces. While a single I-beam of steel was deflected several feet in each direction by their oscillator, and they reportedly felt the bridge shaking many yards away, there were no "earth shattering" effects. It is worth indicating that, in the time of the event undertaken by Tesla, buildings were not built to withstand such resonance. See also
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This article is licensed under the GNU Free Documentation License. It uses material from Wikipedia Encyclopedia article "Resonance Frequency" |
