 WHEN A FORCE
 IS APPLIED REPEATEDLY
 AT THE NATURAL FREQUENCY
 OF ANY SYSTEM,
 LARGE AMPLITUDE
 OSCILLATIONS RESULT.
 THIS IS THE PHENOMENON
 OF RESONANCE.
HAVE YOU EVER
SEEN A SINGER
BREAK A WINEGLASS
WITH HIS VOICE?
I WILL DO THAT TODAY.
IT'S VERY DIFFICULT,
EVEN IF YOU HAVE
A MAGNIFICENT VOICE LIKE MINE.
YOU NEED
A VERY SPECIAL WINEGLASS.
IT MUST BE THIN
AND DELICATE,
AND HAVE
A VERY PURE TONE.
IF YOU TAP IT,
IT MUST GO "PING"
AND NOT "THUNK."
THAT CAN BE SUMMED UP
IN JUST TWO WORDS--
VERY EXPENSIVE.
SO I ASKED
THE PHYSICS DEPARTMENT
TO BUY ME
A VERY EXPENSIVE WINEGLASS.
THEY SAID,
"DRINK OUT OF A PAPER CUP."
I SAID, "NO. IT'S
FOR A DEMONSTRATION."
THEY APPOINTED A COMMITTEE.
THEN THE COMMITTEE MET
AND THOUGHT ABOUT IT.
FINALLY THEY DECIDED
TO APPROPRIATE ENOUGH MONEY
TO BUY ONE EXPENSIVE WINEGLASS
TO BREAK FOR YOU,
AND HERE IT IS.
BUT BEFORE I DO IT,
I WILL EXPLAIN
WHY IT'S GOING TO HAPPEN.
IT HAS TO DO WITH
A PHENOMENON CALLED RESONANCE.
ON THE 1st OF JULY, 1940,
A DELEGATION OF CITIZENS
MET IN WASHINGTON STATE.
THE WEATHER WAS BEAUTIFUL,
THE OCCASION HISTORIC,
AND THE SPEECHMAKING
AND FANFARE
ALTOGETHER APPROPRIATE.
THIS WAS THE GRAND OPENING
OF THE TACOMA NARROWS BRIDGE.
FROM THE BEGINNING,
THE BRIDGE,
WHICH SPANNED PUGET SOUND
BETWEEN SEATTLE AND TACOMA,
WAS TRAVELED IN STYLE,
AS WELL IT
SHOULD HAVE BEEN.
THE TACOMA NARROWS BRIDGE
WAS ONE OF THE LONGER
SUSPENSION BRIDGES ON EARTH.
AND, IF SOMEBODY HADN'T
OVERLOOKED SOMETHING,
IT PROBABLY
WOULD HAVE REMAINED
ONE OF THE LONGER
SUSPENSION BRIDGES ON EARTH.
THE PROBLEM WASN'T THAT,
FROM THE BEGINNING,
PEOPLE DIDN'T PAY ATTENTION
TO DETAILS.
THEY DID.
BUT SOMEWHERE
ALONG THE LINE,
AND THIS WAS OBVIOUS
IN THE END,
IT LOOKS AS IF
SOMEONE FORGOT
THE SIGNIFICANCE...
OF RESONANCE.
RESONANCE.
JUST AS ITS SOUND
LINGERS IN THE AIR,
THE WORD ITSELF
REMAINS IN THE LANGUAGE.
RESONANCE, FROM A LATIN NOUN
MEANING AN ECHO.
BUT RESONANCE CONJURES UP
MORE THAN LINGUISTIC ECHOES.
IN BATTLE, FOR EXAMPLE,
ONE HEARS OF
THE RESOUNDING VICTORY.
BUT SETTING
CONNOTATIONS ASIDE,
RESONANCE CAN BE SEEN AS
A SIMPLE MECHANICAL PRINCIPLE
OF THE PHYSICAL WORLD.
[PLAYING BEETHOVEN SYMPHONY]
PLEASANT SOUNDS
ARE USUALLY PLEASANT
PRECISELY BECAUSE
OF THE WAY THEY RESONATE.
OF COURSE,
ARTISTRY IS A FACTOR.
SO ARE COMPOSITION,
SETTING, AND MOOD.
BUT RESONANCE IS ESSENTIAL.
WITH A VIOLIN OR CELLO,
THE STRINGS' VIBRATIONS
AT HUNDREDS TO THOUSANDS
OF CYCLES PER SECOND
CAUSE THE INSTRUMENT TO VIBRATE
AT THE SAME FREQUENCY.
EVERY VIBRATION GIVES
THE INSTRUMENT'S SOUND BOX
A TINY PUSH
SO THAT THE SOUND BOX
VIBRATES RESONANTLY.
IN TURN, THOSE VIBRATIONS
EXCITE RESONANT VIBRATIONS
OF THE AIR
INSIDE THE SOUND BOX.
THE QUALITY
OF A FINE INSTRUMENT
LIES PRECISELY IN ITS ABILITY
TO RESONATE EQUALLY
WITH EVERY NOTE
THAT'S PLAYED.
WHEN A VIBRATING SYSTEM
IS PUSHED OR DRIVEN
AT THE NATURAL FREQUENCY
OF THAT SYSTEM,
RESONANCE OCCURS.
INSIDE A PIANO,
VIBRATING STRINGS
MAKE THE SOUND BOARD RESONATE.
THIS RESONANCE
IS BEING DRIVEN
BY THE NATURAL FREQUENCY
OF THE STRING,
WHICH IS ABOUT 256 PUSHES
PER SECOND AT MIDDLE C.
EACH TIME
THE STRING IS STRUCK,
IT MAKES THOUSANDS
OF OSCILLATIONS,
EACH ONE ADDING
TO THE RESONANT RESPONSE
OF THE SOUND BOARD.
REPEATEDLY PUSHING
AN OSCILLATING SYSTEM,
WITH EVEN A SMALL FORCE
EACH TIME,
MAKES SUCCESSIVE OSCILLATIONS
GROW BIGGER AND BIGGER.
THE RESULTS ARE VIBRATIONS
OF INCREASED AMPLITUDE.
EVEN IF THESE PUSHES
ARE QUITE SMALL,
RESONANCE WILL RESULT.
THIS VIBRATING TUNING FORK
SETS THE SURROUNDING
AIR MOLECULES
INTO HARMONIC MOTION.
BECAUSE AIR WORKS
AS AN ELASTIC MEDIUM,
IT'S A GOOD CONDUCTOR
OF TRAVELING OSCILLATIONS,
OR WAVES.
EACH OSCILLATION
GENTLY AND RHYTHMICALLY
PUSHES AGAINST THE AIR,
SENDING OUT WAVES
AT THE NATURAL FREQUENCY
OF THE TUNING FORK.
WHEN THE PITCH
OF THE NOTE STRUCK ON THE PIANO
IS THE SAME AS THAT
OF THE TUNING FORK,
EVEN IF THE FORK
ISN'T STRUCK,
WAVES FROM THE PIANO
CAN DISTURB IT
AND SET IT INTO MOTION
BY MEANS OF RESONANCE.
THE TUNING FORK
AND THE PIANO STRING
ARE EXAMPLES OF NATURALLY
OSCILLATING SYSTEMS.
AND THOUGH THEY APPEAR
MORE COMPLICATED,
THEY OBEY
THE SAME DIFFERENTIAL EQUATION
AS THE SIMPLE MASS
ON A SPRING.
LIKE A MASS ON A SPRING,
THEY HAVE
AN INTERNAL FORCE, F,
THAT NATURALLY OPPOSES
ANY DISTURBANCE, x.
THAT MEANS
A DIFFERENTIAL EQUATION...
WHOSE SOLUTION
IS A SINE FUNCTION,
REPRESENTING OSCILLATIONS
AT A NATURAL FREQUENCY,
OMEGA NAUGHT,
THAT DEPENDS ON
THE CHARACTERISTICS
OF THE SYSTEM.
THEY ARE, IN THIS CASE,
k, THE STIFFNESS
OF THE SPRING,
AND m, THE MASS
OF THE BOBBING OBJECT.
THIS IS
ANOTHER OSCILLATING SYSTEM
WITH A NATURAL FREQUENCY.
IN FACT,
THE CHILD AND THE SWING
ARE A KIND OF PENDULUM.
THE FREQUENCY MAY BE
A THOUSAND TIMES LOWER
THAN THE FREQUENCY
OF AUDIBLE SOUND,
BUT THE PRINCIPLE'S
THE SAME.
A SLIGHTLY LARGER MASS,
THIS ONE
WITH LONGER LEGS,
HAS LEARNED TO PROVIDE
HER OWN PERIODIC PUSH
BY SHIFTING HER WEIGHT,
KICKING FORWARD
AS FAR AS POSSIBLE,
AND TUCKING
HER LEGS UNDER.
CORRECTLY APPLIED AT
THE SAME POINT ON EACH CYCLE,
THAT IS, IN PHASE,
THIS YOUNG SWINGER
DISPLAYS HER MASTERY
OF THE PHENOMENON
OF RESONANCE.
BUT A TRUE MASTERY
OF THE PHENOMENON
IS BEST ACHIEVED BY STARTING
WITH AN OSCILLATING FORCE
THAT DOESN'T PRODUCE RESONANCE.
 WHETHER A SWING
 OR A SPRING,
 OSCILLATORS HAVE
THEIR NATURAL UPS AND DOWNS,
 PRODUCED BY
 THE INTERNAL FORCE, F.
 IF AN ADDITIONAL FORCE,
 PROPORTIONAL TO F NAUGHT
 IS APPLIED AT A DIFFERENT
 FREQUENCY OMEGA,
 THE RESULT IS
A MORE COMPLICATED MOTION.
 AND A MORE COMPLICATED
 DIFFERENTIAL EQUATION.
 BUT THE MOTION IS REALLY
 JUST TWO SIMPLE MOTIONS
 ADDED TOGETHER...
 WHICH SOLVE
THE DIFFERENTIAL EQUATION...
 LEAVING AN EQUATION FOR A,
 WHICH IS THE SIZE
 OF THE NEW OSCILLATIONS
 PRODUCED BY
 THE ADDITIONAL FORCE.
 THE SIZE OF THESE OSCILLATIONS
 DEPENDS ON HOW BIG
 THE FORCE IS, a NAUGHT,
 AND ON HOW CLOSE
 ITS FREQUENCY, OMEGA,
IS TO THE NATURAL FREQUENCY,
 OMEGA NAUGHT.
HERE ARE SOME KEY ELEMENTS
OF RESONANCE--
A FORCEFUL VOICE,
EXQUISITE CONTROL
OF FREQUENCY...
CAN THE VOICE
OF ELLA FITZGERALD
SHATTER THIS GLASS?
AND, AN OSCILLATING SYSTEM.
 WHETHER IT'S A WINEGLASS
 OR A SPRING,
 THE AMPLITUDE
 OF FORCED OSCILLATIONS
IS SENSITIVE
TO THE FREQUENCY.
A FORCE AT
LOW FREQUENCY,
OMEGA,
DRIVING
AN OSCILLATOR
OF NATURAL
FREQUENCY,
OMEGA NAUGHT,
CAUSES COMPLICATED,
BUT TINY VIBRATIONS.
AT HIGHER
FREQUENCY,
THE VIBRATIONS GET
A LITTLE BIGGER.
 BUT IF OMEGA
GETS CLOSE TO
OMEGA NAUGHT,
EVEN IF THE FORCE
IS VERY SMALL,
SOME PRETTY
SPECTACULAR THINGS
CAN START
TO HAPPEN.
ADDED TO
THE NATURAL MOTION,
A LOW-FREQUENCY FORCE
HAS ITS EFFECT.
AT HIGHER FREQUENCY,
THE EFFECT CAN BE
MORE INTERESTING.
BUT IF OMEGA GETS CLOSE
TO OMEGA NAUGHT,
THE EFFECT CAN BE
POSITIVELY SHATTERING.
♪ DEE DEE DAA DAA DUM ♪
CAN THE VOICE
OF ELLA FITZGERALD
SHATTER THIS GLASS?
♪ WEEEE! ♪
BELIEVE IT.
ONLY A TINY OSCILLATING FORCE
IS APPLIED TO THIS GLASS,
EVEN THOUGH
THE POWER BEHIND IT
IS ELLA FITZGERALD'S
MAGNIFICENT VOICE.
BUT IT TAKES AN EQUATION
TO SHOW WHY A SINGER
WITH POWER AND CONTROL
CAN HAVE
SUCH A SHATTERING IMPACT.
OF COURSE,
THE DIFFERENTIAL EQUATION
DOES LEAVE OUT
A FEW INTERESTING DETAILS.
ONE OF THE MORE INTERESTING
IS THAT GLASS ITSELF
IS A VISCOUS FLUID,
A VERY, VERY VISCOUS FLUID.
IN FACT,
GLASS IS SO VISCOUS,
IT TAKES CENTURIES
TO FLOW,
TO FLOW DOWNWARD
THROUGH TIME AND SPACE,
WHERE IT SETTLES ALONG
THE THICKER BOTTOM OF THE PANE.
GLASS IS SO VISCOUS
THAT IT SEEMS
SOLID INDEED,
AND EVEN
RINGS AND RESONATES.
OF COURSE, IT'S THE VISCOSITY
OF THE GLASS
THAT PREVENTS
ITS RESONANT OSCILLATIONS
FROM BECOMING INFINITE.
AND WITHOUT THAT VISCOSITY,
THERE WOULDN'T BE
AN UNBROKEN PIECE OF GLASS LEFT
IN EITHER THE OLD WORLD...
OR THE NEW,
WHERE THE EFFECTS OF RESONANCE
CAN BE SEEN
AND HEARD, JUST AS WELL.
FOR EXAMPLE,
WHILE MUSIC IS GENERALLY
A PLEASING EXAMPLE
OF RESONANCE,
THE SAME CAN'T
ALWAYS BE SAID
FOR THE COMMON RHYTHMS
OF CONTEMPORARY SOCIETY.
AS AN ANNOYING EXAMPLE
OF RESONANCE,
CONSIDER
THE VIBRATING WINDOW.
[JETS ROARING]
AT THE SAME TIME, HOWEVER,
WHILE THE PANES MAY SHAKE
THE LISTENER TO DISTRACTION,
BUILT-IN FRICTION
AND VISCOSITY
USUALLY KEEP THEM
FROM SHATTERING.
SOMETIMES,
AS STUDIED INSIDE
THE CALTECH SEISMIC
LABORATORIES IN PASADENA,
THE EFFECTS OF RESONANCE
ARE MORE THAN ANNOYING.
THEY CAN BE DEVASTATING
BECAUSE THEY CAN AMPLIFY
WHAT IS
ALREADY AN ELEMENTAL,
ALMOST IRRESISTIBLE
FORCE OF NATURE.
DURING AN EARTHQUAKE,
SEISMIC WAVES ARE SENT OUT
FROM THE EPICENTER
IN A RANGE OF FREQUENCIES.
COMPARED TO AUDIBLE SOUND,
THESE FREQUENCIES
ARE GENERALLY VERY LOW.
AT EARTHQUAKE FREQUENCIES,
BUILDINGS BETWEEN
5 AND 40 STORIES TALL
ARE TYPICALLY RESONANT.
WHEN THESE MODEL BUILDINGS
ARE SHAKEN
AT A GIVEN FREQUENCY
IN A SIMULATED EARTHQUAKE,
ONE OR ANOTHER
IS SET INTO RESONANT VIBRATION,
DEPENDING ON THE FREQUENCY.
GENERALLY SPEAKING,
A COMPLICATED STRUCTURE
LIKE A BUILDING
WILL SHAKE
OR TWIST RESONANTLY
AT A NUMBER
OF NATURAL FREQUENCIES.
ENGINEERS CAN MINIMIZE
RESONANT RESPONSES
BY DESIGNING ISOLATION
AND ENERGY ABSORPTION
INTO THE BUILDING.
AND WITH STRICT ADHERENCE
TO EARTHQUAKE ORDINANCES,
A STRUCTURE HAS A WAY
TO RESIST BEING RIPPED APART
AT ITS VERY FOUNDATIONS.
BUILDING CODES ARE LAWS.
WHEN PEOPLE THINK SOME LAWS
ARE MADE TO BE BROKEN,
SOME BUILDINGS ARE BOUND
TO SUFFER THE CONSEQUENCES.
[HIGH-PITCHED SOUNDS]
THESE SOUNDS, PRODUCED BY
THE WIND ACTING ON THE WIRE,
ARE ANOTHER EFFECT
OF RESONANCE.
THESE WIRES
SING THEIR SONG
BY VIBRATING AT
THEIR NATURAL FREQUENCY...
BECAUSE, TO MAKE
SOME RATHER SIMPLE MUSIC,
THE AIRFLOW
AROUND A TAUT WIRE
CREATES SOME RATHER
COMPLEX PATTERNS.
PERHAPS TELEPHONE WIRES ONLY
REALLY SING IN MYSTERY STORIES,
IN FICTION,
WHERE THEIR EERIE LYRIC
HARMONIZES WITH
THE HOWLING WIND.
BUT SHOULD TELEPHONE WIRES
EVER SING IN FACT,
THEIR SONG
WILL BE A COMPOSITION
OF THE PHENOMENON OF RESONANCE
AND THE EVER-PRESENT WIND.
IN HIGH WINDS,
THE NORMALLY STABLE AIRFLOW
AROUND A CYLINDER--
THIS WIRE, FOR EXAMPLE--
BECOMES UNSTABLE.
AS THE WIND TRIES
TO CLOSE UP THE GAP
ON THE DOWNWIND SIDE
OF THE WIRE,
TO PREVENT A VACUUM,
EDDIES START TO FORM.
SOON, THE EDDIES
START PEELING OFF,
RUNNING IN
THE DOWNSTREAM WAKE,
CREATING
A PREDICTABLE FLOW PATTERN.
EVERY TIME
A VORTEX PEELS OFF,
IT GIVES THE WIRE
A LITTLE PUSH.
AT A CERTAIN WIND SPEED,
THE VORTICES
START PEELING OFF
AT A RESONANT FREQUENCY
OF THE WIRE,
SETTING IT INTO MOTION.
THIS EFFECT IS CALLED
AN AEOLIAN HARP.
THE SKILL IT WOULD TAKE
TO TUNE THESE STRINGS
WAS HANDED DOWN
FROM THE AEOLIANS,
THE ANCIENT GREEK TRIBES
WHICH SETTLED ON
THE COAST OF ASIA MINOR.
BUT THE SKILL IT TAKES
TO PLAY THE AEOLIAN HARP
COMES FROM THE MAGIC FINGERS
OF THE WIND,
WHEN AIR BLOWS
ACROSS THE STRINGS.
THE PRINCIPLE
OF THE AEOLIAN HARP--
THE PHENOMENON
CALLED RESONANCE--
EXPLAINS THE DRAMATIC SONG
OF WIRES IN THE WIND.
PERHAPS,
AMONG OTHER THINGS,
THE TACOMA NARROWS BRIDGE
WAS THE MOST SPECTACULAR
AEOLIAN HARP IN HISTORY.
UNFORTUNATELY,
ITS FIRST PERFORMANCE
WAS DESTINED TO RUN
ONLY ABOUT FOUR MONTHS.
IN THE MEANTIME,
SHE WAS A BEAUTIFUL BRIDGE.
BEAUTIFUL,
BUT A LITTLE STRANGE.
EVEN BEFORE CONSTRUCTION
WAS COMPLETED,
PEOPLE OBSERVED
ITS PECULIAR BEHAVIOR.
THAT WAS BECAUSE,
EVEN IN A LIGHT BREEZE,
RIPPLES RAN
ALONG THE BRIDGE.
AFTER A WHILE,
ONE OF THE LOCAL HUMORISTS
CALLED HER "GALLOPING GERTIE."
FOR FAIRLY OBVIOUS REASONS,
THE NAME STUCK,
AT LEAST UNTIL
THE 7th OF NOVEMBER, 1940.
THEN, AS NOW,
SEATTLE AND TACOMA
WERE SPORTS-MINDED CITIES.
FOR FOUR MONTHS,
A REGIONAL SPORT
WAS CROSSING THE BRIDGE
ON A WINDY DAY.
WHILE SOME CLAIMED IT WAS LIKE
RIDING A ROLLER COASTER,
OTHERS FOUND IT
DISCONCERTING
TO SEE THE CAR
IN FRONT DISAPPEAR.
HOW POPULAR
THIS BRIDGE SPORT WAS,
OR HOW FAR IT MIGHT HAVE SPREAD
ACROSS THE COUNTRY,
IS ANYBODY'S GUESS.
ON NOVEMBER 7, 1940,
THE WINDS
WERE RELATIVELY MODERATE--
ABOUT 40 MILES PER HOUR.
A NEW MODE APPEARED.
RATHER THAN RIPPLE,
THE BRIDGE BEGAN TO TWIST.
A WIND OF 40 MILES PER HOUR
IS NOT TOO STRONG.
BUT IT WAS STRONG ENOUGH
TO START THE BRIDGE
TWISTING VIOLENTLY.
AND, AT 11 A.M.,
IT FELL.
INVESTIGATORS WERE MYSTIFIED.
A BRIDGE CONSTRUCTED
ACCORDING TO
THE BEST ENGINEERING STANDARDS
OF THE DAY,
PERHAPS THE BEST BRIDGE
IN THE WORLD,
WAS NOT SUPPOSED
TO COLLAPSE.
WHAT IN THE WORLD
HAD HAPPENED?
THEODORE VON KARMAN,
A CALTECH PROFESSOR,
AND A PIONEER
IN MODERN AERODYNAMICS,
PROVIDED THE ANSWER.
VON KARMAN'S EXPLANATION
OF VORTEX SHEDDING
AND RESONANT OSCILLATIONS,
WAS NOT UNIVERSALLY POPULAR
AMONG CONSTRUCTION ENGINEERS.
HOWEVER, AS VERIFIED BY
WIND TUNNEL TESTS AT CALTECH
AND AT
THE UNIVERSITY OF WASHINGTON,
VON KARMAN'S EXPLANTION
WAS CORRECT.
AND EVER SINCE,
NO MAJOR BRIDGE IS COMPLETED
WITHOUT FIRST PASSING
THE TEST OF THE WIND TUNNEL.
THE TIME HAS COME
TO BREAK THE WINEGLASS.
I WON'T DO IT
WITH MY VOICE.
MY CONTRACT WITH THE MET
WON'T PERMIT THAT.
AND THERE'S
ANOTHER PROBLEM.
THIS TAKES PRACTICE,
AND I ONLY HAVE
ONE WINEGLASS.
SO I'LL TRY IT FIRST
USING THIS ORDINARY BEAKER.
HERE'S HOW
IT'S GOING TO WORK.
THIS STUFF
WILL SUBSTITUTE FOR ME
AND MAKE A PURE TONE.
THAT WILL MAKE
THE BEAKER VIBRATE.
THIS MICROPHONE IS LISTENING TO
WHAT THE BEAKER DOES.
THE MICROPHONE'S OUTPUT
IS ON THIS OSCILLOSCOPE.
YOU'LL SEE
WHAT THE BEAKER DOES.
[PING]
YOU SEE THAT?
[PING]
OK.
WHAT I HAVE TO DO
IS TURN UP THE VOLUME,
AND THAT MAKES
THE BEAKER VIBRATE.
THE BEAKER IS VIBRATING,
BUT NOT VERY MUCH
BECAUSE IT'S NOT EXACTLY
AT THE RIGHT FREQUENCY.
IT MUST BE AT
THE BEAKER'S RESONANT FREQUENCY
IN ORDER TO VIBRATE ENOUGH
TO MAKE IT BREAK.
I'LL TUNE THIS
TO THE RIGHT FREQUENCY.
THERE IT IS
RIGHT THERE.
THAT'S IT.
ALL RIGHT.
ALL I HAVE TO DO IS
TURN UP THE VOLUME,
AND IT WILL
BREAK THE BEAKER.
YOUR EARS
WILL BLEED A LITTLE.
HERE WE GO!
SO WE MANAGED TO DO IT
WITHOUT EVER BREAKING
THIS EXQUISITE WINEGLASS.
THEY KNEW
I'D NEVER BREAK IT.
THAT'S IT FOR TODAY.
CAPTIONING PERFORMED BY
THE NATIONAL CAPTIONING
INSTITUTE, INC.
CAPTIONS COPYRIGHT 1985
CALIFORNIA INSTITUTE
OF TECHNOLOGY
THE CORPORATION FOR
COMMUNITY COLLEGE TELEVISION
AND THE ANNENBERG/CPB PROJECT
PUBLIC PERFORMANCE OF CAPTIONS
PROHIBITED WITHOUT PERMISSION OF
NATIONAL CAPTIONING INSTITUTE
Annenberg Media
♪
For information
about this
and other Annenberg
Media programs
call 1-800-LEARNER
and visit us at
www.learner.org.
