Resonance - Real-life applications

A Child on a Swing and a Pendulum in a Museum

Suppose a father is pushing his daughter on a swing, so that she glides back and forth through the air. A swing, as noted earlier, is a classic example of an oscillator. When the child gets in the seat, the swing is in a position of stable equilibrium, but as the father pulls her back before releasing her, she is at maximum displacement.

He releases her, and quickly, potential energy becomes kinetic energy as she swings toward the position of stable equilibrium, then up again on the other side. Now the half-cycle is repeated, only in reverse, as she swings backward toward her father. As she reaches the position from which he first pushed her, he again gives her a little push. This push is essential, if she is to keep going. Without friction, she could keep on swinging forever at the same rate at which she begun. But in the real world, the wearing of the swing's chain against the support along the bar above the swing will eventually bring the swing itself to a halt.

TIMING THE PUSH.

Therefore, the father pushes her—but in order for his push to be effective, he must apply force at just the right moment. That right moment is the point of greatest amplitude—the point, that is, at which the father's pushing motion and the motion of the swing are in perfect resonance.

If the father waits until she is already on the downswing before he pushes her, not all the energy of his push will actually be applied to keeping her moving. He will have failed to efficiently add energy to his daughter's movement on the swing. On the other hand, if he pushes her too soon—that is, while she is on the upswing—he will actually take energy away from her movement.

If his purpose were to bring the swing to a stop, then it would make good sense to push her on the upswing, because this would produce a cycle of smaller amplitude and hence less energy. But if the father's purpose is to help his daughter keep swinging, then the time to apply energy is at the position of maximum displacement.

It so happens that this is also the position at which the swing's speed is the slowest. Once it reaches maximum displacement, the swing is about to reverse direction, and, therefore, it stops for a split-second. Once it starts moving again, now in a new direction, both kinetic energy and speed increase until the swing passes through the position of stable equilibrium, where it reaches its highest rate.

THE FOUCAULT PENDULUM.

Hanging from a ceiling in Washington, D.C.'s Smithsonian Institution is a pendulum 52 ft (15.85 m) long, at the end of which is an iron ball weighing 240 lb (109 kg). Back and forth it swings, and if one sits and watches it long enough, the pendulum appears to move gradually toward the right. Over the course of 24 hours, in fact, it seems to complete a full circuit, moving back to its original orientation.

There is just one thing wrong with this picture: though the pendulum is shifting direction, this does not nearly account for the total change in orientation. At the same time the pendulum is moving, Earth is rotating beneath it, and it is the viewer's frame of reference that creates the mistaken impression that only the pendulum is rotating. In fact it is oscillating, swinging back and forth from the Smithsonian ceiling, but though it shifts orientation somewhat, the greater component of this shift comes from the movement of the Earth itself.

This particular type of oscillator is known as a Foucault pendulum, after French physicist Jean Bernard Leon Foucault (1819-1868), who in 1851 used just such an instrument to prove that Earth is rotating. Visitors to the Smithsonian, after they get over their initial bewilderment at the fact that the pendulum is not actually rotating, may well have another question: how exactly does the pendulum keep moving?

As indicated earlier, in an ideal situation, a pendulum continues oscillating. But situations on Earth are not ideal: with each swing, the Foucault pendulum loses energy, due to friction from the air through which it moves. In addition, the cable suspending it from the ceiling is also oscillating slightly, and this, too, contributes to energy loss. Therefore, it is necessary to add energy to the pendulum's swing.

Surrounding the cable where it attaches to the ceiling is an electromagnet shaped like a donut, and on either side, near the top of the cable, are two iron collars. An electronic device senses when the pendulum reaches maximum amplitude, switching on the electromagnet, which causes the appropriate collar to give the cable a slight jolt. Because the jolt is delivered at the right moment, the resonance is perfect, and energy is restored to the pendulum.

Resonance in Electricity and Electromagnetic Waves

Resonance is a factor in electromagnetism, and in electromagnetic waves, such as those of light or radio. Though much about electricity tends to be rather abstract, the idea of current is fairly easy to understand, because it is more or less analogous to a water current: hence, the less impedance to flow, the stronger the current. Minimal impedance is achieved when the impressed voltage has a certain resonant frequency.

NUCLEAR MAGNETIC RESONANCE.

The term "nuclear magnetic resonance" (NMR) is hardly a household world, but thanks to its usefulness in medicine, MRI—short for magnetic resonance imagining—is certainly a well-known term. In fact, MRI is simply the medical application of NMR. The latter is a process in which a rotating magnetic field is produced, causing the nuclei of certain atoms to absorb energy from the field. It is used in a range of areas, from making nuclear measurements to medical imaging, or MRI. In the NMR process, the nucleus of an atom is forced to wobble like a top, and this speed of wobbling is increased by applying a magnetic force that resonates with the frequency of the wobble.

The principles of NMR were first developed in the late 1930s, and by the early 1970s they had been applied to medicine. Thanks to MRI, physicians can make diagnoses without the patient having to undergo either surgery or x rays. When a patient undergoes MRI, he or she is made to lie down inside a large tube-like chamber. A technician then activates a powerful magnetic field that, depending on its position, resonates with the frequencies of specific body tissues. It is thus possible to isolate specific cells and analyze them independently, a process that would be virtually impossible otherwise without employing highly invasive procedures.

LIGHT AND RADIO WAVES.

One example of resonance involving visible and invisible light in the electromagnetic spectrum is resonance fluorescence. Fluorescence itself is a process whereby a material absorbs electromagnetic radiation from one source, then re-emits that radiation on a wavelength longer than that of the illuminating radiation. Among its many applications are the fluorescent lights found in many homes and public buildings. Sometimes the emitted radiation has the same wavelength as the absorbed radiation, and this is called resonance fluorescence. Resonance fluorescence is used in laboratories for analyzing phenomena such as the flow of gases in a wind tunnel.

Though most people do not realize that radio waves are part of the electromagnetic spectrum, radio itself is certainly a part of daily life, and, here again, resonance plays a part. Radio waves are relatively large compared to visible light waves, and still larger in comparison to higher-frequency waves, such as those in ultraviolet light or x rays. Because the wavelength of a radio signal is as large as objects in ordinary experience, there can sometimes be conflict if the size of an antenna does not match properly with a radio wave. When the sizes are compatible, this, too, is an example of resonance.

MICROWAVES.

Microwaves occupy a part of the electromagnetic spectrum with higher frequencies than those of radio waves. Examples of microwaves include television signals, radar—and of course the microwave oven, which cooks food without applying external heat. Like many other useful products, the microwave oven ultimately arose from military-industrial research, in this case, during World War II. Introduced for home use in 1955, its popularity grew slowly for the first few decades, but in the 1970s and 1980s, microwave use increased dramatically. Today, most American homes have microwaves ovens.

Of course there will always be types of food that cook better in a conventional oven, but the beauty of a microwave is that it makes possible the quick heating and cooking of foods—all without the drying effect of conventional baking. The basis for the microwave oven is the fact that the molecules in all forms of matter are vibrating. By achieving resonant frequency, the oven adds energy—heat—to food. The oven is not equipped in such a way as to detect the frequency of molecular vibration in all possible substances, however; instead, the microwaves resonant with the frequency of a single item found in nearly all types of food: water.

Emitted from a small antenna, the microwaves are directed into the cooking compartment of the oven, and, as they enter, they pass a set of turning metal fan blades. This is the stirrer, which disperses the microwaves uniformly over the surface of the food to be heated. As a microwave strikes a water molecule, resonance causes the molecule to align with the direction of the wave. An oscillating magnetron, a tube that generates radio waves, causes the microwaves to oscillate as well, and this, in turn, compels the water molecules to do the same. Thus, the water molecules are shifting in position several million times a second, and this vibration generates energy that heats the water.

Microwave ovens do not heat food from the inside out: like a conventional oven, they can only cook from the outside in. But so much energy is transferred to the water molecules that conduction does the rest, ensuring relatively uniform heating of the food. Incidentally, the resonance between microwaves and water molecules explains why many materials used in cooking dishes—materials that do not contain water—can be placed in a microwave oven without being melted or burned. Yet metal, though it also contains no water, is unsafe.

Metals have free electrons, which makes them good electrical conductors, and the presence of these free electrons means that the microwaves produce electric currents in the surfaces of metal objects placed in the oven. Depending on the shape of the object, these currents can jump, or arc, between points on the surface, thus producing sparks. On the other hand, the interior of the microwave oven itself is in fact metal, and this is so precisely because microwaves do bounce back and forth off of metal. Because the walls are flat and painted, however, currents do not arc between them.

Resonance of Sound Waves

A highly trained singer can hit a note that causes a wine glass to shatter, but what causes this to happen is not the frequency of the note, per se. In other words, the shattering is not necessarily because of the fact that the note is extremely high; rather, it is due to the phenomenon of resonance. The natural, or resonant, frequency in the wine glass, as with all objects, is determined by its shape and composition. If the singer's voice (or a note from an instrument) hits the resonant frequency, there will be a transfer of energy, as with the father pushing his daughter on the swing. In this case, however, a full transfer of energy from the voice or musical instrument can overload the glass, causing it to shatter.

Another example of resonance and sound waves is feedback, popularized in the 1960s by rock guitarists such as Jimi Hendrix and Pete Townsend of the Who. When a musician strikes a note on an electric guitar string, the string oscillates, and an electromagnetic device in the guitar converts this oscillation into an electrical pulse that it sends to an amplifier. The amplifier passes this oscillation on to the speaker, but if the frequency of the speaker is the same as that of the vibrations in the guitar, the result is feedback.

Both in scientific terms and in the view of a music fan, feedback adds energy. The feedback from the speaker adds energy to the guitar body, which, in turn, increases the energy in the vibration of the guitar strings and, ultimately, the power of the electrical signal is passed on to the amp. The result is increasing volume, and the feedback thus creates a loop that continues to repeat until the volume drowns out all other notes.

How Resonance Can Break a Bridge

The power of resonance goes beyond shattering a glass or torturing eardrums with feedback; it can actually destroy large structures. There is an old folk saying that a cat can destroy a bridge if it walks across it in a certain way. This may or may not be true, but it is certainly conceivable that a group of soldiers marching across a bridge can cause it to crumble, even though it is capable of holding much more than their weight, if the rhythm of their synchronized footsteps resonates with the natural frequency of the bridge. For this reason, officers or sergeants typically order their troops to do something very unmilitary—to march out of step—when crossing a bridge.

The resonance between vibrations produced by wind and those of the structure itself brought down a powerful bridge in 1940, a highly dramatic illustration of physics in action that was captured on both still photographs and film. Located on Puget Sound near Seattle, Washington, the Tacoma Narrows Bridge was, at 2,800 ft (853 m) in length, the third-longest suspension bridge in the world. But on November 7, 1940, it gave way before winds of 42 mi (68 km) per hour.

It was not just the speed of these winds, but the fact that they produced oscillations of resonant frequency, that caused the bridge to twist and, ultimately, to crumble. In those few seconds of battle with the forces of nature, the bridge writhed and buckled until a large segment collapsed into the waters of Puget Sound. Fortunately, no one was killed, and a new, more stable bridge was later built in place of the one that had come to be known as "Galloping Gertie." The incident led to increased research and progress in understanding of aerodynamics, harmonic motion, and resonance.

WHERE TO LEARN MORE

Beiser, Arthur. Physics, 5th ed. Reading, MA: Addison-Wesley, 1991.

Berger, Melvin. The Science of Music. Illustrated by Yvonne Buchanan. New York: Crowell, 1989.

"Bridges and Resonance" (Web site). <http://instruction.ferris.edu/loub/media/BRIDGE/Bridge.html> (April 23, 2001).

"Resonance" (Web site). <http://hyperphysics.phyastr.gsu.edu/hbase/sound/reson.html> (April 26, 2001).

"Resonance" (Web site). <http://www.exploratorium.edu/xref/phenomena/resonance.html> (April 23, 2001).

"Resonance." The Physics Classroom (Web site). <http://www.glenbrook.k12.il.us/gbssci/phys/Class/sound/u11l5a.html> (April 26, 2001).

"Resonance Experiment" (Web site). <http://131.123.17.138/> (April 26, 2001).

"Resonance, Frequency, and Wavelength" (Web site). <http://www.cpo.com/CPOCatalog/SW/sw_b1.html> (April 26, 2001).

Suplee, Curt. Everyday Science Explained. Washington, D.C.: National Geographic Society, 1996.

"Tacoma Narrows Bridge Disaster" (Web site). <http://www.enm.bris.ac.uk/research/nonlinear/tacoma/tacoma.html> (April 23, 2001).