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Chapter 2 The nature of sound（第2页）

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。

9。　>

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）。