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Chapter 2 The nature of sound（第2页）

&fallsonaseriesofparallelliripes，esasihapart（orthereabouts），itisdiffradsierwaveleedthrles，suchdifiragratingssplitwhitelightintoitspocolours—thebaakesrainbowsfromsunbeamsinjustthisway.Siularseriesof‘stripes’ofincreasedpressure，italsoactasadiffragrating，sglightwithawavelengtharoundthatofthedistaripes（thatdistanghalfthewavelengthofthesound）.Usuallythemediumhereisaesolid，suchasfusedquartz.Thisacousto-opticeffect，wheresouerlight，isusedbothuerandinairasaurbiandimagingtool（seeFigure7）.

6.Difiraofdifierehs.

Whensoundsfrommultiplesourcesmeet，mix，aheresultisathree-dimensionalpatternofloudaareasierareasformatthepoiionsfromoaiveinterfereheloudonesarisewheiorarefapressiopressions（struterference）（Figure8）.

Interferenceisimportantinstereosoundprodudinnoise，anditintrodueterthatcharacterizesasousphase，thatis，howhighorlowitspressureisatapartitiime.Phasereallyonlymatterswhensoueratheaboveexample，

7.　Theacousto-opticefiect.

8.　struddestruterference.

pairsofsoundwaveswhosepressionscidewitheachother（andhencemakealoudarea）areihoseinwhichtheydonotcideareoutofphase.Whenwavesaremaximallyoutofphase，theyaresaidtobeinantiphase.systemsotdetectphase.

Thepowerofsound

Thereareseveralwaysinwhichtheamountofsoundbedefinedandmeasured，andeachriatefordifferentapplis.Ifhearingormusicisthetext，soundpressureistheobviousceitistheparameterwhichrelatesmostdirectly（thoughoosimply:readon!）totheimpressionofloudindisgtheeficyofasoundsouraywishtoknowhowmuergyisflowingfromitihesouodescribetheeffectsofapartidfieldoheparameterofihesouy，whichistheamountofsystriking1squaremetreofthatobjecteaeisanill-definedmeasureusedtolabelaudioequipment，butiomimiess.

Audible-frequendwavesloseverylittleehroughabsorptiohroughwhichtheypass（around0.25dB6pertper1hvaryihweathers）.Themainreasonsouhdistatheyarefreetospreadoutinmaions，siesspreadprogressivelymoreaoerandlargervolumes.Ifasoundsourceissuspendedihatitssoundspreadiion（sphericalspreadihesoundpressureisinverselyproportioaehesource:thatis，ifthedistaneasurementpoihesoundpressurehalves.

&yofthesoundfallsmorerapidlythanthis:itisinverselyproportionaltothesquareofthedistance.So，ifthedistaneasurementpoihesouyfallstooer（122）.Ifthedistaipliedby10，theiyfallstooh（1102）.Ifthesouheground，thereadhemispherically（Box5），andsoundpressureayfallathalftheaboverates:iheiyfallstoone-halfifthedistancedhly，

Box5

Sphericalspreading:I=P4pr2;iyI，powerP，distahesourcer.

&hegroureflearblefloorisprettyensitywillfallfasterthanthis，duetolossyduetoabsorption.Thesoundpowerdependsonlyonthesource，soitisthesameatanydistance.

&onesareneverfoundiareperhapsmostcloselyapproximatedbythesongsofbirds.Thewaveformsofrealsoundslookverydifferent:thepressure-plotsofdifferentsoundsofsimilarfualfrequencyareshowninFigure9.

Thedifficultdecibel

Souhefirstformsytobeuood:asfarbackas300bceitwasknowntobesomekindofpatternofphysigesthatcouldtravelthroughairawaslohatthemostobviouscharacteristid—itsloudness—wasquantifiedinanyway.Whatdidturnuptookover2，000yearstoarrive，andwasisfaitdid.

Byfarthemostwidelyusedwaytoquaofsoundisthedecibel（dB，Box6）:iftwosignalsdifferinsoundpressureby1dB，theratioofthosepressuresisabout1.2:1.（Handily，thishappehesmallestdifferenhearuions.）A10dBdiffereoaratioofabout3:1，anda100dBdiffereioof100，000:1.

Adecibelisohofabel，anamemadebybiersoransmissiontheory（（β，ε，andl）ofthehattoAlexanderGrahamBell.Decibelsaren’tuios，sotheydesorepowerfulohingisthananother:youcould，ifyouwished，usethemtoparetheoutputsofapairofheaters.Butthatwouldnottellyouanythingabouthowhoteitherofthemactuallyare.

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Box6

&hesoundpowerdifferendecibelsbetweensoundsofpo0is10log10（P1P0）.Powerisproportionaltopressuresquared，sothesoundpressurediffereweensoundpressuresp1andp2is10log10（p12p22），whichis20log10（p1p2）.

&hesoundofadevidecibels，itisvitaltoknowaringitwith.Forairborheparisoniswithasoundthatisjusthearable（dingtoapressureoftwentymicropascals）.Wheofsouermsofsucharefereheword‘level’isappended:hendpressurelevel（SPL），forexample.So，asoundof0dBis‘oimeslouderthan’（i.e.equallyloudas）asoundyoujustabouthear，1dBisabout1:12timesasloud，2dBis1:26times，andsoon.Areallashappywiththissolutio.Ultrasouuch‘louderthanyoujustabouthear’theirultrasoundis，beooiplace.It’spowertheylike，andit’swattstheymeasureitin.Meanwhile，uisrightlyask:‘Thethreshold?Whatdoesthatmeanwhenyourearsarefullofwateraarubberheadpie?Orifyou’reawhale?’Sotheybasetheirdeareferencepressureofonemicropascal，becausethat’soremember.Sowokindsofdeeforuseinwaterandoneforair，whichwillgivedifferehesamesound.Nottoomuchofaproblemsolongaseveryonealwaysrememberstosaywhatthereferehedecibeltheyareusingis.Sadlyhowever，theydon’t.

&herproblem.Fewofusudaproduces—anttoknowishowlouditwillsound.Andthatdependsonhowfarawaythethingis.Thismayseemobvious，butitmeaeversaythattheSPLofais90dB，onlythatithasthatvalueatsomestateddistahosehassopopularibooksgetthisbitwrong，andclaimtheSPLofapicdrillis100dB，whentheyreallymean‘100dBifmeasuredatadistanceof10（orhoweverma’snotdificulttoseewherethislazihechartsusuallyalsohaveexampleslike‘aquietofidweuhatthechartmakerisreferringtoaquietoficethatyin，ofithecorridororiown.

&hirdproblem:asourightmakesouanyoahandfuloratawidevarietyoffreque’sassumeforthemomentthatthesourceofthesoundisaloudspeakersoefitthatitalwaysvertsalltheeleergyfedintoitintosou’simagihasafrequentrolbutnovolumeknob.Ifwemeasuredthetotalsyflowingfromthatloudspeakeread（thatis，thepower）whilegitsfrequency，thatpowerwouldofaint.Similarly，theSPLataparticulardistaheloudspeakerwouldstaythesame—asamiewouldshow（assumingitwereequallyseallfrequencies）.

&hisisnothiyourearswouldtellyou.Iftheloudspeakerwasjustaudibleat20Hz，itwouldinloudhefrequeilataround4kHzitwouldshly）200timeslherfrequeill，itwouldgetquieteragain，finallyfadingintoinaudibilityatsomewherebetween8kHzand20kHz，dependinghowoldyouareandwhatyou’vebeendoingtoyourearsforthepastfe>

Iisweighttherespoofwhichthemisapart，sothatthesystembehavesliketheear—beiofrequearound4kHz.Afrequeedmieistheheartofasouer（SLM）.Thereisactuallyawidechoicehtings，inefs，butthemostpopularbyfarisA-weighting，roximatestheresponseofahumamoderatesoundlevels.HehedecibelsthatmattertousareusuallyA-weighted，writtendBA，thefullnameforwhichis‘A-levelweightedsoundpressurelevelindecibels’.

SLMsareequippedwithaeiionfactors.Thismattersbecauseifasoundlastslessthanabout0.1seditsouer，sihehearingsystemaddsuptheenergyforaboutthisperiod.

Toaddtotheplexity，theloudnessofasoundalsodepeureofitssourstance，peoplesodislikethesoundofpla，e，theysiderthemtobeasannoyingasanonymoussoundsthatareabout5dBlouder.versely，peopleareratherfondoftraiheextentthattheyonlyfinditasannoyingasanonymoussoundswhichareabout5dBquieter.Thesereasaresowellestablishedthatmanyplanningappliswhivolveaircraftorrailwayheirfiguresby5dB（thesareknowmalusandtherailwaybonus）.Thismeansthatuallymeasurewhatarchiteeowners，noiseers，noisymaebuyers，andasreallyoknow:howloudasoundis.

gallofthis，thereislittlepointinmeasuringSPLswithgreatacsareaccurateto+–1.4dBat10kHz（calledClass2meters）.Eveninlaboratorywork，+–1.1dBat10kHzisalmostalwaysenough（asprovidedbyaClass1SLM）.Farmoreimportantthanaccuracyisadhereaprocedures，ingthefrequentsbyparisonwithstamies.

&heplexitiesofloudsvariatitothesourdtheuser，extensivesurveysofthereasenumbersofindividualstocarefullysouerminedroughlyhowloudoSPL，andunitshavebeehisbasis，inparticularthephon.PhonsaredefinedashavingthesamevaluesastheSPLsof1kHztones，soa1kHztohanSPLof10dBhasaloudenphons.Buta50HztohatsameloudenphonshasanSPLof73dB，becauseourearsaresomuchlessse50Hzthan1kHzthata50Hztoobe63dBhigherthana1kHztoosoundasloud.

Loudnessisjustoneesetofpsyeasures，alsoknownassoundqualityparameters（‘quality’beihesenseof‘character’ratherthan‘goodness’）.Loudnessisbyfarthemostonlyusedadeveloped;theothersincludesharpness（inacums），roughness（aspers），flu（vaddieselness（whiounits:differentautomobilesaresimplyraivelyagtohow‘dieselly’peoplethinktheysound）.Asthelast-s，thesemeasuresweredevelopedprimarilybytheautomotiveindustryiomakedoor-ginesounds，aornoisessoundappropriatelypowerful，mase，reliable，andsoon.Inpriwouldbeveryusefulifdomesticprodudothernoisesourcescouldbecharacterizedbysuchparameters.

&opidqualitiesispartofthediseofpsychoacoustics，thestudyofthepsychologicaleffectsofsound，whichitselfsideredasaofwhatisnowknownassoundstudies.Soundstudiesdealwithhowsoundsofallkindshavebeenmadeahroughouthistoryandiures.Workonsuchtopicshasbeesihe1940s，andhasilysiheearly1990s.

Standing>

Aregaimioryofacoustiakesouhe1780s，Ernstistudiedthewaysiesvibratewheo‘sirokedwithaviolinbow.Finepowderspriheplatesisdefleareaswherevibrati，ahosethatarestill.Thepowder-free，strpoioahepeakshsinFigure1），aionary，powderyareasaretheswherethereisne（wheretheliheaxisinFigure1）.