笔趣看

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。