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BASICDECIBELSindB’sByMartyMcCann©2006PeaveyElectronicsCorporationBASICDECIBELSTheDecibelScaleinvolveschangesintheelectricalgain(volume),ortheamplificationoftheaudiosignal,thatresultsinchangesintheloudnessoftheSoundPressureLevel(SPL),perceivedbythelistener.TheDecibelScaleandPerceptionGainchangesindBandhowwehearthemandtheresultantchangesinsystempowerandvoltagetotheloudspeaker:DecibelsdBChangesin:AudibleDecibelPerceptionPowerVoltage+dBJustNoticeableTimes%+dBModerateTimes%+dBTwiceasLoudTimes%DecibelsdBChangesin:AudibleDecibelPerceptionPowerVoltage+3dBJustNoticeable2Times40%+6dBModerate4Times100%+10dBTwiceasLoud10Times300%DecibelsinSpecificationsLoudspeakerFrequencyResponse:50Hz-17.5kHz+/-3dBPowerAmplifierFrequencyResponse:10Hz-20kHz+/-0.5dBCommonModeRejectionRatio:-100dBEquivalentInputNoise:-129dBEqualizationorToneControlRangeofBoost&Cut:+/-15dBSignaltoNoise:-105dBCrossoverSlope:-24dB/OctaveAmplifierGain:30dBPowerAmpSensitivity:1.4dBLoudspeaker1Watt1MeterSensitivity:101dBDynamicRange:120dB0dBV=1volt0dBm=0.77456volts@600Ohms0dBw=1Wattor2.828voltsinto8Ohms2006NIGERIANPROAUDIOSYMPOSIUMLAGOSNovember2006ListentoThisRalph“C”ElectronicsLtdINTERMEDIATEDECIBELSTheDecibels’mostImportantuseinSystemDesign:TheInverseSquareLaw&HighFrequencyCDHorn-6dBPatternsofCoverageInverseSquareLaw:•Thesoundeminatingdirectlyfromasourcewillchangeinsoundpressurelevel(SPL),directlyproportionaltotheinverseofthesquareofthedistanceawayfromthesource.AREAOFACIRCLE:=RadiusSquaredxPiAREAOF1/2CIRCLE:=1/2RadiusSquaredxPir=4mA=16x3.1416A=50.2656Sqmr=8mA=64x3.1416A=201.0624A=1/2(r^2x3.1416)201.0624/4=50.2656AREAOF1/2CIRCLERadiusArea4m=25.1328Sqm8m=100.5312Sqm16m=402.1248Sqm32m=1,608.4992SqmAREAOFASPHERE:=4xRadiusSquaredxPiAREAOF1/2ASPHERE:=2xRadiusSquaredxPir=4mA=2x16x3.1416A=100.5312Sqmr=8mA=2x64x3.1416A=402.1248SqmA(1/2Sphere)=2(r^2x3.1416)402.1248/4=100.5312AREAOF1/2SPHERERadiusArea4m=100.5312Sqm8m=402.1248Sqm16m=1,608.4992Sqm32m=6,433.9968SqmInverseSquareLawSimplified:Sounddrops-6dBinlevel(SPL)eachtimeyoudoublethedistanceawayfromthesource.dBlosswithDistance2Meters=-6dB4Meters=-12dB10Meters=-20dB20Meters=-26dB32Meters=-30dBLosswithDistanceinFeet10Feet=-10dB20Feet=-16dB40Feet=-22dB80Feet=-28dB160Feet=-34dBConstantDirectivityHorns•ConstantDirectivityHorns’angleofcoveragearedeterminedbythe-6dBdownpointsofthehornintheHorizontalandVerticalplanes.•Theanglesofcoveragearethepointsthatmeasure-6dBlessthantheon-axismeasurement.6.5Ft7Degrees11.5Ft52.5Ft100dB65.9Ft11.5-52.5Feet=+/-3dB81.9dB75.8dB13Ft52.9Ft96dBLineArrayExceptiontotheInverseSquareLaw•TrueLineArrayscreateaCylindricalwavefront.•Thereductioninlevelwithdistanceissaidtobe-3dBwitheachdoublingofdistance,butgenerallyismorelike-4dB.•Eventhenitisfrequencydependentanddropsofflessandlessasyougolowerinfrequency.ListentoThisAdvancedDecibelsandSoundEngineeringByMartyMcCann©2006PeaveyElectronicsCorporationBase10LogarithmsInvolvethenumber10raisedtosomeexponentialvalue.Suchas:•10tothe1stPwr=10•10tothe2ndPwr=100•10tothe3rdPwr=1,000•10tothe4thPwr=10,000•10tothe5thPwr=100,000•10tothe6thPwr=1,000,000•10tothe7thPwr=10,000,00010BaseNotation•10tothe8thPwr=100,000,000•10tothe9thPwr=1,000,000,000•10tothe10thPwr=10,000,000,000NotethattheExponentorPwr#isalsothenumberofzero’stotherightofthe1.10totheXPwrnotation•Makesmultiplicationanddivisioneasy.•Inlonghandmultiplication:10,000x1,00000000000000000010000____10,000,00010totheXPwrnotation•Indecibel(10^X)notationweAddexponentstomultiply:10tothe4thPwr(10,000)+10tothe3thPwr(1,000)=10tothe7thPwr(10,000,000)10tothe-XPwrnotation•10tothe-1Pwr=0.1•10tothe-2Pwr=0.01•10tothe-3Pwr=0.001•10tothe-4Pwr=0.0001•10tothe-5Pwr=0.00001Notethatwithnegativeexponents,thePwrrepresentsthenumberofplacestotherightofthedecimalpoint.Nowthatisassimpleaswecanmakedecibels....Asinactualityitcangethairybecausetheexponentialvaluecanhaveit’sowndecimalpointinit....Suchas:10tothe1.2659Pwror10tothe-0.3697PwrLogarithms•ForCenturieswehadtorelyupon100’sofpagesofLogtablesthatcouldbefoundinthebackofMathbooks.•Thatisupuntilabout1972whenHewlettPackardintroducedthefirsthandheldcalculator,themodelSR-10.LoudspeakerSensitivityat1Wattat1Meter=100dB1Watt=100dB2Watt=103dB4Watt=106dB8Watt=109dB16Watt=112dB32Watt=115dB64Watt=118dB128Watt=121dB256Watt=124dBTenTimesPower=+10dB1Watt=100dBat1Meter10Watt=110dBat1Meter100Watt=120dBat1MeterOneHundredTimesPower=+20dB1Watt=100dBat1Meter100Watt=120dBat1MeterBackto+3dBforTwoTimesPower100Watt=120dBat1Meter200Watt=123dBat1Meter300Watt=124.5dBat1Meter(Guesstimate)300Wattsat1Meter=124.5dB1Meter=124.5dB2Meter=118.5dB4Meter=112.5dB8Meter=106.5dB16Meter=100.5dBCalculatingDecibelsforPower•10LogP1/P2•10LogP2/P1•10Log(FullPowerratedinWatts)/1Watt•SystemGain=10LogFullPower(ratinginWatts)FullPowerGainofLoudspeaker10Log300=GainatFullPowerLog300=2.47710x2.477=24.8dBat300Watts(at1Meter)CalculatingDecibelsforDistance•20LogX1/X2•Distance=D•20LogD2/D1•20Log(DistanceinMeters)/1Meter•LosswithDistance=20LogDistance(inMeters)LossatDistanceof16Meters20Log16=LossinSPLat16MetersLog16=1.220x1.2=(-)24dBFinalCalculation:Se