Science of Everyday Things Vol. 2 - Physics Episode 10 pps

experi-encing oscillation, frequency is the number of cycles that take place during one second.. In wave motion, frequency is the number of waves passing through a given pointduring the

Frequency If an object in harmonic motion has a

fre-quency of 50 Hz, its period is 1/50 of a second(0.02 sec) Or, if it has a period of 1/20,000 of asecond (0.00005 sec), that means it has a fre-quency of 20,000 Hz

The frequency of a pendulum, a swing-likeoscillator, is the number of “swings” per minute

Its frequency is proportional to the square root ofthe downward acceleration due to gravity (32 ft

or 9.8 m/sec2) divided by the length of the dulum This means that by adjusting the length

pen-of the pendulum on the clock, one can change itsfrequency: if the pendulum length is shortened,the clock will run faster, and if it is lengthened,the clock will run more slowly

Another variety of pendulum, this one ing to the early nineteenth century, is ametronome, an instrument that registers thetempo or speed of music Consisting of a pendu-lum attached to a sliding weight, with a fixedweight attached to the bottom end of the pendu-lum, a metronome includes a number scale indi-cating the frequency—that is, the number ofoscillations per minute By moving the upperweight, one can speed up or slow down the beat

dat-Harmonics

As noted earlier, the volume of any sound isrelated to the amplitude of the sound waves Fre-quency, on the other hand, determines the pitch

or tone Though there is no direct correlationbetween intensity and frequency, in order for aperson to hear a very low-frequency sound, itmust be above a certain decibel level

The range of audibility for the human ear isfrom 20 Hz to 20,000 Hz The optimal range forhearing, however, is between 3,000 and 4,000 Hz

This places the piano, whose 88 keys range from

27 Hz to 4,186 Hz, well within the range ofhuman audibility Many animals have a muchwider range: bats, whales, and dolphins can hearsounds at a frequency up to 150,000 Hz Buthumans have something that few animals canappreciate: music, a realm in which frequencychanges are essential

Each note has its own frequency: middle C,for instance, is 264 Hz But in order to producewhat people understand as music—that is, pleas-ing combinations of notes—it is necessary toemploy principles of harmonics, which expressthe relationships between notes These mathe-matical relations between musical notes areamong the most intriguing aspects of the con-nection between art and science

It is no wonder, perhaps, that the great Greekmathematician Pythagoras (c 580-500 B.C.)believed that there was something spiritual ormystical in the connection between mathematicsand music Pythagoras had no concept of fre-quency, of course, but he did recognize that therewere certain numerical relationships between thelengths of strings, and that the production ofharmonious music depended on these ratios

R A T I O S O F F R E Q U E N C Y A N D

P L E A S I N G T O N E S Middle C—located,,appropriately enough, in the middle of a pianokeyboard—is the starting point of a basic musi-cal scale It is called the fundamental frequency,

or the first harmonic The second harmonic, oneoctave above middle C, has a frequency of 528

Hz, exactly twice that of the first harmonic; andthe third harmonic (two octaves above middle C)has a frequency of 792 cycles, or three times that

of middle C So it goes, up the scale

As it turns out, the groups of notes that ple consider harmonious just happen to involvespecific whole-number ratios In one of thosecurious interrelations of music and math thatwould have delighted Pythagoras, the smaller thenumbers involved in the ratios, the more pleasingthe tone to the human psyche

peo-An example of a pleasing interval within anoctave is a fifth, so named because it spans fivenotes that are a whole step apart The C Majorscale is easiest to comprehend in this regard,because it does not require reference to the “blackkeys,” which are a half-step above or below the

“white keys.” Thus, the major fifth in the Major scale is C, D, E, F, G It so happens that the

C-AMPLITUDE: For an object oscillation,amplitude is the value of the object’s max-imum displacement from a position of sta-ble equilibrium during a single period In atransverse wave, amplitude is the distancefrom either the crest or the trough to theaverage position between them For asound wave, the best-known example of alongitudinal wave, amplitude is the maxi-mum value of the pressure change betweenwaves.

when the oscillating particle moves from acertain point in a certain direction, thenswitches direction and moves back to theoriginal point Typically, this is from theposition of stable equilibrium to maxi-mum displacement and back again to thestable equilibrium position

experi-encing oscillation, frequency is the number

of cycles that take place during one second

In wave motion, frequency is the number

of waves passing through a given pointduring the interval of one second In eithercase, frequency is measured in Hertz

Period (T) is the mathematical inverse of frequency (f) hence f=1/T.

movement of a particle about a position ofequilibrium, or balance

fre-quency, named after nineteenth-centuryGerman physicist Heinrich Rudolf Hertz

(1857-1894) Higher frequencies areexpressed in terms of kilohertz (kHz; 103

or 1,000 cycles per second); megahertz(MHz; 106or 1 million cycles per second);

and gigahertz (GHz; 109or 1 billion cyclesper second.)

an object possesses due to its motion, aswith a sled when sliding down a hill This iscontrasted with potential energy

which the movement of vibration is in thesame direction as the wave itself This iscontrasted to a transverse wave

object in oscillation, maximum ment is the farthest point from stable equi-librium

motion, typically periodic, in one or moredimensions

PERIOD: In oscillation, a period is theamount of time required for one cycle For

a transverse wave, a period is the amount

of time required to complete one full cycle

of the wave, from trough to crest and back

to trough In a longitudinal wave, a period

is the interval between waves Frequency is

the mathematical inverse of period (T):

hence, T=1/f.

repeated at regular intervals These vals are known as periods

inter-K E Y T E R M S

Frequency

that an object possesses due to its position,

as, for instance, with a sled at the top of

a hill This is contrasted with kinetic energy

in which, if an object were disturbed, itwould tend to return to its original posi-tion For an object in oscillation, stableequilibrium is in the middle of a cycle,

between two points of maximum placement

which the vibration or motion is cular to the direction in which the wave ismoving This is contrasted to a longi-tudinal wave

motion that carries energy from one place

to another without actually moving anymatter

K E Y T E R M S C O N T I N U E D

ratio in frequency between middle C and G (396Hz) is 2:3

Less melodious, but still certainly tolerable,

is an interval known as a third Three steps upfrom middle C is E, with a frequency of 330 Hz,yielding a ratio involving higher numbers thanthat of a fifth—4:5 Again, the higher the num-bers involved in the ratio, the less appealing thesound is to the human ear: the combination E-F,with a ratio of 15:16, sounds positively grating

The Electromagnetic Spectrum

Everyone who has vision is aware of sunlight,but, in fact, the portion of the electromagneticspectrum that people perceive is only a small part

of it The frequency range of visible light is from4.3 • 1014 Hz to 7.5 • 1014Hz—in other words,from 430 to 750 trillion Hertz Two things should

be obvious about these numbers: that both therange and the frequencies are extremely high Yet,the values for visible light are small compared tothe higher reaches of the spectrum, and the range

is also comparatively small

Each of the colors has a frequency, and thevalue grows higher from red to orange, and so onthrough yellow, green, blue, indigo, and violet

Beyond violet is ultraviolet light, which humaneyes cannot see At an even higher frequency are

x rays, which occupy a broad band extendingalmost to 1020Hz—in other words, 1 followed by

20 zeroes Higher still is the very broad range

of gamma rays, reaching to frequencies as high as 1025 The latter value is equal to 10 trilliontrillion

Obviously, these ultra-ultra high-frequencywaves must be very small, and they are: the high-

er gamma rays have a wavelength of around 10-15meters (0.000000000000001 m) For frequencieslower than those of visible light, the wavelengthsget larger, but for a wide range of the electro-magnetic spectrum, the wavelengths are stillmuch too small to be seen, even if they were vis-ible Such is the case with infrared light, or therelatively lower-frequency millimeter waves.Only at the low end of the spectrum, withfrequencies below about 1010Hz—still an incred-ibly large number—do wavelengths become thesize of everyday objects The center of themicrowave range within the spectrum, forinstance, has a wavelength of about 3.28 ft (1 m)

At this end of the spectrum—which includes television and radar (both examples ofmicrowaves), short-wave radio, and long-waveradio—there are numerous segments devoted tovarious types of communication

R A D I O A N D M I C R O W A V E F R E

-Q U E N C I E S The divisions of these sections

of the electromagnetic spectrum are arbitraryand manmade, but in the United States—wherethey are administered by the Federal Communi-cations Commission (FCC)—they have the force

of law When AM (amplitude modulation) radiofirst came into widespread use in the early

1920s—Congress assigned AM stations the

fre-quency range that they now occupy: 535 kHz to

1.7 MHz

A few decades after the establishment of theFCC in 1927, new forms of electronic communi-

cation came into being, and these too were

assigned frequencies—sometimes in ways that

were apparently haphazard Today, television

tions 2-6 are in the 54-88 MHz range, while

sta-tions 7-13 occupy the region from 174-220 MHz

In between is the 88 to 108 MHz band, assigned

to FM radio Likewise, short-wave radio (5.9 to

26.1 MHz) and citizens’ band or CB radio (26.96

to 27.41 MHz) occupy positions between AM

and FM

In fact, there are a huge variety of frequencyranges accorded to all manner of other commu-

nication technologies Garage-door openers and

alarm systems have their place at around 40

MHz Much, much higher than these—higher, in

fact, than TV broadcasts—is the band allotted to

deep-space radio communications: 2,290 to

2,300 MHz Cell phones have their own realm, of

course, as do cordless phones; but so too do radio

controlled cars (75 MHz) and even baby

DiSpezio, Michael and Catherine Leary Awesome

Experi-ments in Light and Sound New York: Sterling

<http://www.howstuffworks.com/radio~spec-Internet Resources for Sound and Light (Web site).

<http://electro.sau.edu/SLResources.html> (April 25, 2001).

“NIST Time and Frequency Division.” NIST: National Institute of Standards and Technology (Web site).

<http://www.boulder.nist.gov/timefreq/> (April 25, 2001).

Parker, Steve Light and Sound Austin, TX: Raintree

Frequency

to the cooking of food in a microwave oven.

H O W I T W O R K S

Vibration of Molecules

The possibility of resonance always exists ever there is periodic motion, movement that isrepeated at regular intervals called periods,and/or harmonic motion, the repeated move-ment of a particle about a position of equilibri-

wher-um or balance Many examples of resonanceinvolve large objects: a glass, a child on a swing, abridge But resonance also takes place at a levelinvisible to the human eye using even the mostpowerful optical microscope

All molecules exert a certain

electromagnet-ic attraction toward each other, and generallyspeaking, the less the attraction between mole-cules, the greater their motion relative to oneanother This, in turn, helps define the object inrelation to its particular phase of matter

A substance in which molecules move athigh speeds, and therefore hardly attract one

another at all, is called a gas Liquids are als in which the rate of motion, and hence ofintermolecular attraction, is moderate In a solid,

materi-on the other hand, there is little relative motimateri-on,and therefore molecules exert enormous attrac-tive forces Instead of moving in relation to oneanother, the molecules that make up a solid tend

to vibrate in place

Due to the high rate of motion in gas cules, gases possess enormous internal kineticenergy The internal energy of solids and liquids

mole-is much less than in gases, yet, as we shall see, theuse of resonance to transfer energy to theseobjects can yield powerful results

Oscillation

In colloquial terms, oscillation is the same asvibration, but, in more scientific terms, oscilla-tion can be identified as a type of harmonicmotion, typically periodic, in one or moredimensions All things that oscillate do so eitheralong a more or less straight path, like that of aspring pulled from a position of stable equilibri-um; or they oscillate along an arc, like a swing orpendulum

In the case of the swing or pendulum, stableequilibrium is the point at which the object ishanging straight downward—that is, the posi-tion to which gravitation force would take it if noother net forces were acting on the object For aspring, stable equilibrium lies somewherebetween the point at which the spring isstretched to its maximum length and the point atwhich it is subjected to maximum compressionwithout permanent deformation

C Y C L E S A N D F R E Q U E N C Y Acycle of oscillation involves movement from a

certain point in a certain direction, then a

rever-sal of direction and a return to the original point

It is simplest to treat a cycle as the movement

from a position of stable equilibrium to one of

maximum displacement, or the furthest possible

point from stable equilibrium

The amount of time it takes to complete onecycle is called a period, and the number of cycles

in one second is the frequency of the oscillation

Frequency is measured in Hertz Named after

nineteenth-century German physicist Heinrich

Rudolf Hertz (1857-1894), a single Hertz (Hz)—

the term is both singular and plural—is equal to

one cycle per second

A M P L I T U D E A N D E N E R G Y Theamplitude of a cycle is the maximum displace-

ment of particles during a single period of

oscil-lation When an oscillator is at maximum

dis-placement, its potential energy is at a maximum

as well From there, it begins moving toward the

position of stable equilibrium, and as it does so,

it loses potential energy and gains kinetic energy

Once it reaches the stable equilibrium position,

kinetic energy is at a maximum and potential

energy at a minimum

As the oscillating object passes through theposition of stable equilibrium, kinetic energy

begins to decrease and potential energy increases

By the time it has reached maximum

displace-ment again—this time on the other side of the

stable equilibrium position—potential energy is

once again at a maximum

O S C I L L A T I O N I N W A V E M O

-T I O N The particles in a mechanical wave (a

wave that moves through a material medium)

have potential energy at the crest and trough, and

gain kinetic energy as they move between these

points This is just one of many ways in which

wave motion can be compared to oscillation

There is one critical difference between

oscilla-tion and wave mooscilla-tion: whereas oscillaoscilla-tion

involves no net movement, but merely

move-ment in place, the harmonic motion of waves

carries energy from one place to another

Nonetheless, the analogies than can be made

between waves and oscillations are many, and

understandably so: oscillation, after all, is an

aspect of wave motion

A periodic wave is one in which a uniformseries of crests and troughs follow one after the

other in regular succession Two basic types ofperiodic waves exist, and these are defined by therelationship between the direction of oscillationand the direction of the wave itself A transversewave forms a regular up-and-down pattern, inwhich the oscillation is perpendicular to thedirection in which the wave is moving On theother hand, in a longitudinal wave (of which asound wave is the best example), oscillation is inthe same direction as the wave itself

Again, the wave itself experiences net ment, but within the wave—one of its definingcharacteristics, as a matter of fact—are oscilla-tions, which (also by definition) experience nonet movement In a transverse wave, which isusually easier to visualize than a longitudinalwave, the oscillation is from the crest to thetrough and back again At the crest or trough,potential energy is at a maximum, while kineticenergy reaches a maximum at the point of equi-librium between crest and trough In a longitudi-nal wave, oscillation is a matter of density fluctu-ations: the greater the value of these fluctuations,the greater the energy in the wave

move-A COMMON EXAMPLE OF RESONANCE : A PARENT PUSH

-ES HER CHILD ON A SWING (Photograph by Annie Griffiths Belt/Corbis Reproduced by permission.)

The definitions of these terms vary somewhat,depending on whether one is discussing oscilla-tion or wave motion; or, where wave motion isconcerned, on whether the subject is a transversewave or a longitudinal wave.

For the present purposes, however, it is essary to focus on just a few specifics of harmon-

nec-ic motion First of all, the type of motion with

which we will be concerned is oscillation, andthough wave motion will be mentioned, ourprincipal concern is the oscillations within thewaves, not the waves themselves Second, the twoparameters of importance in understanding res-onance are amplitude and frequency

Resonance and Energy

Transfer

Resonance can be defined as the condition inwhich force is applied to an oscillator at the point

of maximum amplitude In this way, the motion

of the outside force is perfectly matched to that

of the oscillator, making possible a transfer ofenergy

T HE POWER OF RESONANCE CAN DESTROY A BRIDGE O N N OVEMBER 7, 1940, THE ACCLAIMED T ACOMA N ARROWS

B RIDGE COLLAPSED DUE TO OVERWHELMING RESONANCE (UPI/Corbis-Bettmann Reproduced by permission.)

As its name suggests, resonance is a matter ofone object or force “getting in tune with” anoth-

er object One literal example of this involves

shattering a wine glass by hitting a musical note

that is on the same frequency as the natural

fre-quency of the glass (Natural frefre-quency depends

on the size, shape, and composition of the object

in question.) Because the frequencies resonate, or

are in sync with one another, maximum energy

transfer is possible

The same can be true of soldiers walkingacross a bridge, or of winds striking the bridge at

a resonant frequency—that is, a frequency that

matches that of the bridge In such situations, a

large structure may collapse under a force that

would not normally destroy it, but the effects of

resonance are not always so dramatic Sometimes

resonance can be a simple matter, like pushing a

child in a swing in such a way as to ensure that

the child gets maximum enjoyment for the effort

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

exam-ple of an oscillator When the child gets in the

seat, the swing is in a position of stable

equilibri-um, but as the father pulls her back before

releas-ing her, she is at maximum displacement

He releases her, and quickly, potential

ener-gy becomes kinetic enerener-gy 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

lit-tle 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

T I M I N G T H E P U S H Therefore, thefather 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 ofgreatest amplitude—the point, that is, at whichthe father’s pushing motion and the motion ofthe swing are in perfect resonance

If the father waits until she is already on thedownswing before he pushes her, not all theenergy of his push will actually be applied tokeeping her moving He will have failed to effi-ciently add energy to his daughter’s movement

on the swing On the other hand, if he pushes hertoo 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 astop, then it would make good sense to push her

on the upswing, because this would produce acycle of smaller amplitude and hence less energy

But if the father’s purpose is to help his daughterkeep swinging, then the time to apply energy is atthe position of maximum displacement

It so happens that this is also the position atwhich the swing’s speed is the slowest Once itreaches maximum displacement, the swing isabout to reverse direction, and, therefore, it stopsfor a split-second Once it starts moving again,now in a new direction, both kinetic energy andspeed increase until the swing passes through theposition of stable equilibrium, where it reachesits highest rate

T H E F O U C A U LT P E N D U L U M Hanging from a ceiling in Washington, D.C.’sSmithsonian Institution is a pendulum 52 ft(15.85 m) long, at the end of which is an iron ballweighing 240 lb (109 kg) Back and forth itswings, and if one sits and watches it longenough, the pendulum appears to move gradual-

ly toward the right Over the course of 24 hours,

in fact, it seems to complete a full circuit, movingback to its original orientation

There is just one thing wrong with this ture: though the pendulum is shifting direction,this does not nearly account for the total change

pic-in orientation At the same time the pendulum ismoving, Earth is rotating beneath it, and it is theviewer’s frame of reference that creates the mis-taken impression that only the pendulum isrotating In fact it is oscillating, swinging backand forth from the Smithsonian ceiling, butthough it shifts orientation somewhat, thegreater component of this shift comes from themovement of the Earth itself

Resonance This particular type of oscillator is known as

a Foucault pendulum, after French physicist JeanBernard Leon Foucault (1819-1868), who in

1851 used just such an instrument to prove thatEarth is rotating Visitors to the Smithsonian,after they get over their initial bewilderment atthe fact that the pendulum is not actually rotat-ing, may well have another question: how exactlydoes the pendulum keep moving?

As indicated earlier, in an ideal situation, apendulum continues oscillating But situations

on Earth are not ideal: with each swing, the cault pendulum loses energy, due to friction fromthe air through which it moves In addition, thecable suspending it from the ceiling is also oscil-lating slightly, and this, too, contributes to ener-

Fou-gy loss Therefore, it is necessary to add enerFou-gy tothe pendulum’s swing

Surrounding the cable where it attaches tothe ceiling is an electromagnet shaped like adonut, and on either side, near the top of thecable, are two iron collars An electronic devicesenses when the pendulum reaches maximumamplitude, switching on the electromagnet,which causes the appropriate collar to give thecable a slight jolt Because the jolt is delivered atthe right moment, the resonance is perfect, andenergy is restored to the pendulum

Resonance in Electricity and Electromagnetic Waves

Resonance is a factor in electromagnetism, and inelectromagnetic waves, such as those of light orradio Though much about electricity tends to berather abstract, the idea of current is fairly easy tounderstand, because it is more or less analogous

to a water current: hence, the less impedance toflow, the stronger the current Minimal imped-ance is achieved when the impressed voltage has

a certain resonant frequency

N U C L E A R M A G N E T I C R E S O

-N A -N C E The term “nuclear magnetic nance” (NMR) is hardly a household world, butthanks to its usefulness in medicine, MRI—shortfor magnetic resonance imagining—is certainly awell-known term In fact, MRI is simply themedical application of NMR The latter is aprocess in which a rotating magnetic field is pro-duced, causing the nuclei of certain atoms toabsorb energy from the field It is used in a range

reso-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 atop, and this speed of wobbling is increased byapplying a magnetic force that resonates with thefrequency of the wobble

The principles of NMR were first developed

in the late 1930s, and by the early 1970s they hadbeen applied to medicine Thanks to MRI, physi-cians can make diagnoses without the patienthaving to undergo either surgery or x rays When

a patient undergoes MRI, he or she is made to liedown inside a large tube-like chamber A techni-cian then activates a powerful magnetic fieldthat, depending on its position, resonates withthe frequencies of specific body tissues It is thuspossible to isolate specific cells and analyze themindependently, a process that would be virtuallyimpossible otherwise without employing highlyinvasive procedures

L I G H T A N D R A D I O W A V E S Oneexample of resonance involving visible and invis-ible light in the electromagnetic spectrum is res-onance fluorescence Fluorescence itself is aprocess whereby a material absorbs electromag-netic radiation from one source, then re-emitsthat radiation on a wavelength longer than that

of the illuminating radiation Among its manyapplications are the fluorescent lights found inmany homes and public buildings Sometimesthe emitted radiation has the same wavelength asthe absorbed radiation, and this is called reso-nance fluorescence Resonance fluorescence isused in laboratories for analyzing phenomenasuch as the flow of gases in a wind tunnel.Though most people do not realize thatradio waves are part of the electromagnetic spec-trum, radio itself is certainly a part of daily life,and, here again, resonance plays a part Radiowaves are relatively large compared to visiblelight waves, and still larger in comparison tohigher-frequency waves, such as those in ultravi-olet light or x rays Because the wavelength of aradio signal is as large as objects in ordinaryexperience, there can sometimes be conflict if thesize of an antenna does not match properly with

a radio wave When the sizes are compatible, this,too, is an example of resonance

M I C R O W A V E S Microwaves occupy apart of the electromagnetic spectrum with high-

er frequencies than those of radio waves ples of microwaves include television signals,radar—and of course the microwave oven, which

Exam-Resonancecooks 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

Intro-duced for home use in 1955, its popularity grew

slowly for the first few decades, but in the 1970s

and 1980s, microwave use increased

dramatical-ly Today, most American homes have

micro-waves ovens

Of course there will always be types of foodthat 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

vibrat-ing By achieving resonant frequency, the oven

adds energy—heat—to food The oven is not

equipped in such a way as to detect the

frequen-cy of molecular vibration in all possible

sub-stances, however; instead, the microwaves

reso-nant with the frequency of a single item found in

nearly all types of food: water

Emitted from a small antenna, the waves are directed into the cooking compart-

micro-ment 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

ener-gy that heats the water

Microwave ovens do not heat food from theinside out: like a conventional oven, they can

only cook from the outside in But so much

ener-gy is transferred to the water molecules that

con-duction 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

con-tains no water, is unsafe

Metals have free electrons, which makesthem good electrical conductors, and the pres-

ence of these free electrons means that themicrowaves produce electric currents in the sur-faces of metal objects placed in the oven

Depending on the shape of the object, these rents can jump, or arc, between points on thesurface, thus producing sparks On the otherhand, the interior of the microwave oven itself is

cur-in fact metal, and this is so precisely becausemicrowaves do bounce back and forth off ofmetal 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 tohappen is not the frequency of the note, per se Inother words, the shattering is not necessarilybecause of the fact that the note is extremelyhigh; rather, it is due to the phenomenon of res-onance The natural, or resonant, frequency inthe 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 resonantfrequency, there will be a transfer of energy, aswith the father pushing his daughter on theswing In this case, however, a full transfer ofenergy from the voice or musical instrument canoverload the glass, causing it to shatter

Another example of resonance and soundwaves is feedback, popularized in the 1960s byrock guitarists such as Jimi Hendrix and PeteTownsend of the Who When a musician strikes

a note on an electric guitar string, the stringoscillates, and an electromagnetic device in theguitar converts this oscillation into an electricalpulse that it sends to an amplifier The amplifierpasses this oscillation on to the speaker, but ifthe 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 amusic fan, feedback adds energy The feedbackfrom the speaker adds energy to the guitar body,which, in turn, increases the energy in the vibra-tion of the guitar strings and, ultimately, thepower of the electrical signal is passed on to theamp The result is increasing volume, and thefeedback thus creates a loop that continues torepeat until the volume drowns out all othernotes

displace-ment of particles from their normal tion during a single period of oscillation

oscil-lation

experi-encing oscillation, frequency is the number

of cycles that take place during one second

Frequency is measured in Hertz

movement of a particle about a position ofequilibrium, or balance

frequen-cy, named after nineteenth-century man physicist Heinrich Rudolf Hertz(1857-1894) Higher frequencies areexpressed in terms of kilohertz (kHz; 103

Ger-or 1,000 cycles per second) Ger-or megahertz(MHz; 106or 1 million cycles per second.)

an object possesses due to its motion, aswith a sled when sliding down a hill This iscontrasted with potential energy

which the movement of vibration is in thesame direction as the wave itself This iscontrasted to a transverse wave

object in oscillation, maximum ment is the furthest point from stable equi-librium

motion, typically periodic, in one or moredimensions

for one cycle in oscillating motion

repeated at regular intervals These vals are known as periods

uniform series of crests and troughs followone after the other in regular succession

that an object possesses due to its position,

as, for instance, with a sled at the top of ahill This is contrasted with kinetic energy

force is applied to an object in oscillation atthe point of maximum amplitude

fre-quency that matches that of an oscillatingobject

in which, if an object were disturbed, itwould tend to return to its original posi-tion For an object in oscillation, stableequilibrium is in the middle of a cycle,between two points of maximum displace-ment

which the vibration or motion is cular to the direction in which the wave ismoving This is contrasted to a longitudi-nal wave

motion that carries energy from one place

to another without actually moving anymatter

K E Y T E R M S

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

dra-matic illustration of physics in action that was

captured on both still photographs and film

Located on Puget Sound near Seattle,

Washing-ton, 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, butthe fact that they produced oscillations of reso-

nant 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

col-lapsed into the waters of Puget Sound nately, no one was killed, and a new, more stablebridge was later built in place of the one that hadcome to be known as “Galloping Gertie.” Theincident led to increased research and progress inunderstanding of aerodynamics, harmonicmotion, and resonance

Fortu-W H E R E T O L E A R N M O R E

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.

“Resonance.” The Physics Classroom (Web site).

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).

con-without the application of destructive ence to the muffler on an automobile exhaustsystem, for instance, noise pollution from carswould be far worse than it is Other examples ofinterference, both constructive and destructive,can be found wherever there are waves: in water,

interfer-in sound, interfer-in light

H O W I T W O R K S

Waves

Whenever energy ripples through space, there is

a wave In fact, wave motion can be defined as atype of harmonic motion (repeated movement

of a particle about a position of equilibrium, orbalance) that carries energy from one place toanother without actually moving any matter Awave on the ocean is an example of a mechanicalwave, or one that involves matter; but though thematter moves in place, it is only the energy in thewave that experiences net movement

Wave motion is related to oscillation, a type

of harmonic motion in one or more dimensions

There is one critical difference, however: tion involves no net movement, only movement

oscilla-in place, whereas the harmonic motion of wavescarries energy from one place to another Yet,

individual waves themselves are oscillating even

as the overall wave pattern moves

A transverse wave forms a regular down pattern in which the oscillation is perpen-dicular to the direction the wave is moving.Ocean waves are transverse, though they alsohave properties of longitudinal waves In a longi-tudinal wave, of which a sound wave is the bestexample, oscillation occurs in the same direction

up-and-as the wave itself

ed at regular intervals called periods In the case

of wave motion, a period (represented by the

symbol T) is the amount of time required to

complete one full cycle of the wave, from trough

to crest and back to trough

Period can be mathematically related to eral other aspects of wave motion, includingwave speed, frequency, and wavelength Frequen-

sev-cy (abbreviated f) is the number of waves passing

through a given point during the interval of onesecond It is measured in Hertz (Hz), named afternineteenth-century German physicist HeinrichRudolf Hertz (1857-1894), and a Hertz is equal

to one cycle of oscillation per second Higher quencies are expressed in terms of kilohertz(kHz; 103or 1,000 cycles per second) or mega-hertz (MHz; 106or 1 million cycles per second.)Wavelength (represented by the symbol abbrevi-ated λ, the Greek letter lambda) is the distancebetween a crest and the adjacent crest, or a

trough and an adjacent trough, of a wave The

higher the frequency, the shorter the wavelength

Another parameter for describing wavemotion—one that is mathematically independ-

ent from the quantities so far described—is

amplitude, or the maximum displacement of

particles from a position of stable equilibrium

For an ocean wave, amplitude is the distance

from either the crest or the trough to the level

that the ocean would maintain if it were

perfect-ly still

Superposition and

Inter-ference

S U P E R P O S I T I O N The principle ofsuperposition holds that when several individual

but similar physical events occur in close

prox-imity, the resulting effect is the sum of the

mag-nitude of the separate events This is akin to the

popular expression, “The whole is greater than

the sum of the parts,” and it has numerous

appli-cations in physics

Where the strength of a gravitational field isbeing measured, for instance, superposition dic-

tates that the strength of that field at any given

point is the sum of the mass of the individual

particles in that field In the realm of

electromag-netic force, the same statement applies, thoughthe units being added are electrical charges ormagnetic poles, rather than quantities of mass

Likewise, in an electrical circuit, the total current

or voltage is the sum of the individual currentsand voltages in that circuit

Superposition applies only in equations forlinear events—that is, phenomena that involvemovement along a straight line Waves are linearphenomena, and, thus, the principle describesthe behavior of all waves when they come intocontact with one another If two or more wavesenter the same region of space at the same time,then, at any instant, the total disturbance pro-duced by the waves at any point is equal to thesum of the disturbances produced by the indi-vidual waves

I N T E R F E R E N C E The principle ofsuperposition does not require that waves actual-

ly combine; rather, the net effect is as though theywere combined The actual combination or join-ing of two or more waves at a given point in space

is called interference, and, as a result, the wavesproduce a single wave whose properties aredetermined by the properties of the individualwaves

If two waves of the same wavelength occupythe same space in such a way that their crests and

A PIANO TUNER , USING A TUNING FORK SUCH AS THE ONES SHOWN ABOVE , UTILIZES INTERFERENCE TO TUNE THE

INSTRUMENT (Bettmann/Corbis Reproduced by permission.)

troughs align, the wave they produce will have anamplitude greater than that possessed by eitherwave initially This is known as constructiveinterference The more closely the waves are inphase—that is, perfectly aligned—the more con-structive the interference

It is also possible that two or more waves cancome together such that the trough of one meetsthe crest of the other, or vice versa In this case,what happens is destructive interference, and the resulting amplitude is the difference be-tween the values for the individual waves If thewaves are perfectly unaligned—in other words, ifthe trough of one exactly meets the crest of theother—their amplitudes cancel out, and theresult is no wave at all

Resonance

It is easy to confuse interference with resonance,and, therefore, a word should be said about thelatter phenomenon The term resonancedescribes a situation in which force is applied to

an oscillator at the point of maximum tude In this way, the motion of the outside force

ampli-is perfectly matched to that of the oscillator,making possible a transfer of energy As withinterference, resonance implies alignment

between two physical entities; however, there areseveral important differences

Resonance can involve waves, as, forinstance, when sound waves resonate with thevibrations of an oscillator, causing a transfer ofenergy that sometimes produces dramaticresults (See essay on Resonance.) But in thesecases, a wave is interacting with an oscillator, not

a wave with a wave, as in situations of ence Furthermore, whereas resonance entails atransfer of energy, interference involves a combi-nation of energy

interfer-T R A N S F E R V S C O M B I N Ainterfer-T I O N The importance of this distinction is easy to see

if one substitutes money for energy, and peoplefor objects If one passes on a sum of money toanother person, a business, or an institution—as

a loan, repayment of a loan, a purchase, or agift—this is an example of a transfer On theother hand, when married spouses each earnpaychecks, their cash is combined

Transfer thus indicates that the originalholder of the cash (or energy) no longer has it.Yet, if the holder of the cash combines funds withthose of another, both share rights to an amount

of money greater than the amount each

original-ly owned This is analogous to constructive ference

inter-I F THIS BOAT ’ S WAKE WERE TO CROSS THE WAKE OF ANOTHER BOAT , THE RESULT WOULD BE BOTH CONSTRUCTIVE AND DESTRUCTIVE INTERFERENCE (Photograph by Roger Ressmeyer/Corbis Reproduced by permission.)