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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，ahinstrawtoitsdruTheothereraedtotraeonastripofslasswhichwasmovedalongastheearwasshoutedat.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，whoeverspeakstheWhilethesamewordwillbesaiddifferentlybydifferehereareelementswhilyslightly，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.
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