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Chapter 2 The nature of sound（第3页）

Itossibleforito‘see’souhiswayoheydidhroughspace:theywerestationary，or‘standing’waves.Forastandingwave，Figure1representsonlyhowthepressureofthewavegeswithlodhepressureataparticularspote（suchatime-baseddiagramforanypointinastandingwavewouldbeahorizontalline）.

Theprincipleisclearerwhehestandingsouareformedwhenoneblowsacrosstheopenendofa12cmtubewhichisclosedattheotherend.Inallsuchwaves，theairatthedofthetubeove，duetofriwiththeendwall（sothispointisawaveofthiskindisoneinwhichthemotionoftheairmolecreaseswithdistahisend，andreachesamaximum（aheopehiswave，oerofawavelengthisiube，soithasawavelengthof4×12=48eblh，awhewaveswillform，eachwithaohetubeandaheother，asshownihelengthsoftheseotherlemultiplesofthefirst，andsuchwavesareknownasharmonics.

10.　Standingenatoneend.

Justasinsuchapipe，soinanyotherfluid-filledcavity，idobject，therearewavelengthsofsoundarticularlyeasytoexcite.Thesearecalledresonancemodes（orsimplyresohemainoedsiheydependonlyondimensions.Forinstance，ifa12cmrodisfixedatitsendsandstrucksharply，itwillgee24dwaves，togetherwithwavesoflengths12cm，8cm，6cm，4dallotherswhiapart—agaiofharmonics.

A12gboxofairorwaterwillproduceallthesewavestoo—inthiscase，sthe‘ends’ofthefluidmovingisthattheyareadjattotheboxwalls，wherefripreveion.Theboxroducefamiliesofwavesdingtoitsheight，width，anddiagonals.

Resonanbeamajorprobleminroomacoustics，butarethebasisofmostmusistruments.Withaiubesopenatoneend（likesaheopenendisanantinode，ahefualfrequencyhastwicethewavelengthofthatofaclosedtubeofthesamelength.（Actually，theantinodeformsjustbeyondthepipe’send，requiringaneobemade，seeBox7.）

Box7

Usually，thelowestresonahemostpowerful;hreatdealyissuppliedtoamayresoave—oreventwo—higher.Aflute，forexample，willdothisifitisblh（‘overblown’）.

Resonancesareallaroundus—tapaplate，glass，orforkanditwillring，providedonlythatitisnotdampedbybeiightly（tuningforksstillresolybecausetheyhavetwoidentigsthatmoveiions，geachotheroutatthehahereismotiohisisahandywayoffihercrockeryiscracked:ifalliswell，eachsuccessivemillimetreoftheplatewillmoveimmediatelyafteritsneighbmillimetre，alloass，muchlikeaMexilateis，literally，sound.Butifevenaverylinecrackseparatesadjatareas，draggingandfriptheresonangrisetoahy‘k’.

Iftheforcesuppliedtoaisasoufrequency，thegwillbehighlyeficeguitarstringsthatsoundinsympathywiththosestruckacrosstheroom，orbitsoftelevisiobuzzannoyinglyalongrogrammesounds.

&whiportanseveralareasofacousticsisHelmholtzresonance，familiartoanyonewhohasblownacrossthetopofabottletomakeitsing.AnyhollowobjectorcavityenneckwillactasaHelmholtzresonator（Box8）.Ifastreamofairisblownacrosstheopeerthenegthepressureiyalittle.Thisoverpressurepushestheairoutagain—and，justlikeapendulum，

thisair‘overshoots’abit，leavingaslightunderpressure，whichsucksmoreairin，andsoulargstitutesasouaresonantfrequency.Ifasouhisfrequencyissuppliedtotheresonator，itwillsly.

Box8

gsounds

Standingwavesareasmallsubsetofsouly，theregionsofhighandlowpressureihroughspace（suchwavesarecalledprogressivewaves）.Ifoo‘see’atravellingwave，ohereforechartairpressuregesthroughtime.OoattemptthiswasAlexanderGrahamBell，whoin1874proearfromapreghoiltokeepitflexible，ahinstrawtoitsdrum.Theothereraedtotraeonastripofslasswhichwasmovedalongastheearwasshoutedat.Thiswobblyliregofasouhedevicewasearphonautograph.Tothereliefofthosewhohadtostructthem，laterversiohdeadearsinfavourofmetaldiaphragms.

Phonautographswerenactualmeasurementsofsoundwaves，however;thesewereeventuallyprovidedbythecathoderayoscilloscope（CRO），developedinthe1930s.besetwithdifferenttime-basessothatahigh-frequendbespreadoutacrossthesoralowfrequenpressed，sothattheiresbeseen.Fromthis，theirwavelengthsbereadoffandtheirfrequeermined.

11.Spe.

Today，puterizedversionsofCROsarewidelyused.However，atwo-dimensionalplotstillonlydisplaysomefeaturesofsound.Mostsoundidlybothientandinpressure，whilybeproperlydisplayedtogetheronathree-dimensionaldisplay，calledaspe，roduputer.Irhtupthesusuallyrepresentsfrequendbrightnessorcolourrepresentssoundpressure（oriy）.Inothercases，arepresentationofathree-dimensionalshapemaybemadeoheresultsmes（Figure11）.

Unweavingsounds

Beioseeasoundallowsoofindoutalotaboutitqualitatively，androughmeasurementsadeofthesoutputs，butoftengoodquaionaboutsoundisoeliminatenoiseorimprovethedesignofamusistrument）.Forthis，amathematialysisisrequired，awidelyusedaalisbasedonworkductedbyJosephFourierinthe1800s.

Fourierrealizedthatanyperiodi（thatis，onewhichrepeatsatasteadyrate）structedbyaddiheraseries（nowcalledaFourierseries）ofsinewaves—andheworkedoutamethodtodetermihemembers（terms）ofthatseriesare.（MathematicallyspeakingaFourierseriesisposedofaseriesofsinesaaeissimplyasiartsatmaximum，ratherthanatzero，soI’lljustrefertosinewaveshere.）AsFigure12shows，asfewasthreesinewavesroughlyapproximateasquare

Tomakethesidesofthelattermorevertical，higher-frequebeadded.AsquarewavesoundslikeadFourieranalysisshowsthereforethatasudden（thatis，rapidlyinginlevel）clieveryhigh-frequenpos.

12.　Summioapproximateasquare>

Finalplicabletoperiodicwaves，butadevelopmentofitknownastheFouriertransformdlenon-periodies.AhighlyefitmathematicalmethodofgtheposinewavesofasignalisknownasaFastFourierTransform（FFT）.Whenaddihis，theirphasemustbetakenintoat.Duringasihesoundpressureofawaverisesfromzero（thatis，equaltotheambieomaximum，thenfallsdowntominimum，aain.Thisissimilartothevertiofadotpaiheedgewheel，sophasebedestermsofaingat0°thewaverisestoamaximumataphaseof90°，fallstozeroat180°，downtoaminimumat270°，andbacktozeroat360°（whichisthesameas0°）.

Allrealsouime，sotheintosiberepeatedfrequently.Suchtime-varyingfrequenalysesofsoundshavemanyapplis:forinstaheparametersofthesoundwaveswhiposeanindividual’svoiiquetothatperson.Hence，suchparametersbeusedasacoustigerprints’（calledvoits），andautomaticallyreizedbyamae.

versely，sinceeverywordhasauniquesouforhomophoneslike‘sew’and‘so’），itisinprinciplepossibleforamaetically，whoeverspeaksthem.Whilethesamewordwillbesaiddifferentlybydifferehereareelementswhilyslightly，orprediceourabilitytnizeawordirrespective（withinlimits）ofitsspeaker.

Automaticspeeitionisalongerfehowever，andthemainproblemliesindegwhereoheoseehowtrickythisis，trylisteningtoyourselfsaying‘breadandbutter’.Youwillprobablyactuallyhearsomethinglike‘brembudder’withall（andsayingthephrase‘properly’herfeelsnorsoundsnatural）.Thereasonthathumaifywordssoreadilyisthatthesoundpatternswehearareonlyonepieceofevideowhatisbeingsaid—asChapter4>

Soundsfromnowhere

Sinysoundalysedintosifollowsthatanysouhesizedfromthem:sygeespeesoundshavebeenavailableformanyyears，andworkfarbetterthanreizers.Ihough，itisofteogeespeechbyaddiherfragmentsofpre-receedsounds—ateownasvoig.

Usually，however，owantnewsoundsbutimprovedversioingones—amusianofnoise，forexample.Theseleofpre-reentsisalsoonlyusedfornon-speeds:ocelebratedeleicgadgetsforthebuddingpopmusicproduthe1960swastheMellotron（1963）—amaeloadedwithalibraryofshortpiecesofsouomagape，anyofwhichcouldbequicklyseledplayedatafrequene.

&ingsounds:filters

Theowaytomodifysoundisthroughfiltering:theremovalorreduofselectedfrequenges，aplishedeitherbyeleiccircuitsorbysh-passfilterscutoutlowfrequencies，low-passohhighfrequendband-passfiltersbanishboth.Aoncefamiliarkindofvariablefilteristhegraphicequalizer，aseriesofaboutsevensliderbarsonahi-fi’samplifier，whichallowsselectedpresetfrequeobesuppressed.Thesimpler‘torolsimilarlyquieteherhigh（‘treble’）orlow（‘bass’）frequencies.

Avastraherfacilitiesisalsotobefouerizedtoolboxofthesoundartistineer:suchsoftwareaddreverberatio，artifidscape，orapplysuchreal-timegesasshiftingthefrequehesoundsofapbeftoaloudspeaker.Thisisthebasisofakaraokesystem，inwhiotesofsongsbesharpetechthosethattheuserfiosing.