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Formulas of Acoustics PDF

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Formulas Of Acoustics http://forums.freshwap.com/ Formulas of Acoustics F.P.Mechel (Ed.) Formulas of Acoustics SecondEdition Withcontributionsby: M.L.Munjal,M.Vorla¨nder,P.Ko¨ltzsch,M.Ochmann,A.Cummings, W.Maysenho¨lder,W.Arnold 123 Prof.Dr.FridolinP.Mechel Landhausstraße12 71120Grafenau Germany LibraryofCongressControlNumber:2008922894 ISBN:978-3-540-76832-6 Thispublicationisavailablealsoas: ElectronicpublicationunderISBN978-3-540-76833-3 and PrintandelectronicbundleunderISBN978-3-540-76834-0 Thisworkissubjecttocopyright.Allrightsarereserved,whether thewholeorpartofthematerial isconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broad- casting,reproductiononmicrofilmsorinotherways,andstorageindatabanks.Duplication ofthis publication orpartsthereofisonlypermittedundertheprovisionsoftheGermanCopyrightLawof September 9, 1965, in its current version, and permission for use must alwaysbe obtained from Springer-Verlag.ViolationsareliableforprosecutionundertheGermanCopyrightLaw. (cid:2)c Springer-VerlagBerlinHeidelbergNewYork2008 Theuseofregisterednames,trademarks,etc.inthispublicationdoesnotimply,evenintheabsence ofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelawsandregulations andthereforefreeforgeneraluse. SpringerispartofSpringerScience+BusinessMedia springer.com Editor:Dr.ChristophBaumann,KerstinKindler,Heidelberg,Germany DevelopmentEditor:LydiaMueller,Heidelberg,Germany TypesettingandProduction:le-texpublishingservicesoHG,Leipzig,Germany CoverDesign:FridoSteinen-Broo,Girona,Spain Printedonacid-freepaper SPIN:12190720 2109—543210 Preface to the first edition, abbreviated Modern acoustics is more and more based on computations,and computations are based onformulas.Such workneeds previousandcontemporary results.It consumes much time and effort to search needed formulas during the actual work.Therefore, fundamentalsandresultsofacousticsthatcanbeexpressedasformulaswillbecollected inthisbook. Theformulacollectionissubdividedintofieldsofacoustics(Chapters).Forsomefields, in which this author is not expert enough,he invitedco-authors to contribute.Most colleaguescontactedforpossiblecontributionswereconvincedoftheprojectandagreed spontaneously. The material within a field of acoustics is subdivided in Sections which deal with a defined task.Some overlap of Sections should be tolerated; but the subdivision into well-definedSectionswillbehelpfultothereadertofindaparticulartopicofinterest. The present formula collection should not be considered a textbook in a condensed form.Derivationsofapresentedresultwillbedescribedonlyasfarastheyarehelpful inunderstandingtheproblem;themoreinterestedreaderisreferredtothe“source”of theresult.Usefulprinciplesandcomputationalprocedureswillalsobeincluded,evenif theyneed moredescribingtext.SymbolsandquantitieswillbedefinedintheSection, andwhereverusefulasketchwillhelptoexplaintheobjectandthetask. Oneoftheadvantagesofaformulacollectionisseeninuniformdefinitions,notations andsymbolsforquantities.Astrictuniformityintheformofacentrallistofsymbols used never works,according to this author’s observation. Therefore,only commonly used symbols (such as medium density,speed of sound,circular frequency,etc.) are collectedinacentrallistofsymbols(seeConventions);othersymbolsaredefinedinthe relevantchapter. Most Sections contain, below their title or in the text, a reference to the literature. It cannot be the task and intention of this bookeither to indicate time priorities of publicationsconcerningatopicortogiveasurveyoftheexistingliterature.Thereference quotedisthesourceofmoreinformation,whichtheauthorhasused. Highertranscendentalfunctionsusedintheformulaswillbeexplainedbyreferenceto mathematical literature,ifnecessary.Iffunctionsareusedwithdifferentdefinitionsin theliterature,thedefinitionappliedherewillbepresented. The authors think that the bookin its present formcontains most of traditionaland modern results of both fundamental and special character so that the book can be VI Preface helpful to researchers and engineers in the fields of physical acoustics,noise control, androomacoustics. Themanuscriptwaswritteninacamerareadyform(inordertoavoidproofreading). Soprintingerrorsaretheresponsibilityoftheeditingauthor.Hewouldbegratefulfor indicationsofsucherrors. Theauthorgratefullyacknowledgesthesupportgiventotheprojectbytheco-authors andbythepublisher. Grafenau,October2001 Preface to the second edition Thebookwasoutofprintin2004.Theneedofreprintgaveafirstopportunitytoapply some corrections to (rather harmless) misprints and to a few more serious formula errors (the positions of the errors are marked by a footnote∗)).Some of the shown diagramsweregeneratedbythecomputingprogramMathematica(cid:2);thisprogramun- fortunatelyhaslostitsabilitytowriteaxesandplotlabelssothattheycanbeunderstood byreceivingtextprograms.Thereforetransscriptionstoplotlabelsareenumeratednear the diagrams, where necessary. This second edition is moderately enlarged by some additionaltopicsinnewSections. Grafenau,May2008 Contents Prefacetothefirstedition,abbreviated . . . . . . . . . . . . . . . . . . . . . . . . . V Prefacetothesecondedition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VI Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII Contributors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XIX A Conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 B GeneralLinearFluidAcoustics . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 F.P.Mechel B.1 FundamentalDifferentialEquations . . . . . . . . . . . . . . . . . . . . . 5 B.2 MaterialConstantsofAir. . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 B.3 GeneralRelationforFieldAdmittanceandIntensity. . . . . . . . . . . . 11 B.4 IntegralRelations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 B.5 Green’sFunctionsandFormalism . . . . . . . . . . . . . . . . . . . . . . 13 B.6 OrthogonalityofModesinaDuctwithLocallyReactingWalls . . . . . 19 B.7 OrthogonalityofModesinaDuctwithBulkReactingWalls . . . . . . . 20 B.8 SourceConditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 B.9 Sommerfeld’sCondition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 B.10 PrinciplesofSuperposition . . . . . . . . . . . . . . . . . . . . . . . . . . 22 B.11 Hamilton’sPrinciple . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 B.12 AdjointWaveEquation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 B.13 VectorandTensorFormulationofFundamentals . . . . . . . . . . . . . 26 B.14 BoundaryConditionataMovingBoundary . . . . . . . . . . . . . . . . 38 B.15 BoundaryConditionsinLiquidsandSolids . . . . . . . . . . . . . . . . . 39 B.16 CornerConditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 B.17 SurfaceWaveatLocallyReactingPlane . . . . . . . . . . . . . . . . . . . 41 B.18 SurfaceWaveAlongaLocallyReactingCylinder . . . . . . . . . . . . . . 42 B.19 PeriodicStructures,AdmittanceGrid . . . . . . . . . . . . . . . . . . . . 44 B.20 PlaneWallwithWideGrooves . . . . . . . . . . . . . . . . . . . . . . . . . 48 B.21 ThinGridonHalf-InfinitePorousLayer . . . . . . . . . . . . . . . . . . . 50 B.22 GridofFiniteThicknesswithNarrowSlits onHalf-InfinitePorousLayer . . . . . . . . . . . . . . . . . . . . . . . . . 53 B.23 GridofFiniteThicknesswithWideSlits onHalf-InfinitePorousLayer . . . . . . . . . . . . . . . . . . . . . . . . . 56 VIII TableofContents C EquivalentNetworks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 F.P.Mechel C.1 FundamentalsofEquivalentNetworks . . . . . . . . . . . . . . . . . . . . 59 C.2 DistributedNetworkElements . . . . . . . . . . . . . . . . . . . . . . . . 65 C.3 ElementswithConstrictions. . . . . . . . . . . . . . . . . . . . . . . . . . 71 C.4 SuperpositionofMultipleSourcesinaNetwork . . . . . . . . . . . . . . 73 C.5 ChainCircuit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 C.6 PartitionImpedanceofOrifices . . . . . . . . . . . . . . . . . . . . . . . . 74 D ReflectionofSound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 F.P.Mechel D.1 PlaneWaveReflectionataLocallyReactingPlane . . . . . . . . . . . . . 127 D.2 PlaneWaveReflectionatanInfinitelyThickPorousLayer . . . . . . . . 129 D.3 PlaneWaveReflectionataPorousLayerofFiniteThickness . . . . . . . 130 D.4 PlaneWaveReflectionataMultilayerAbsorber . . . . . . . . . . . . . . 132 D.5 DiffuseSoundReflectionataLocallyReactingPlane . . . . . . . . . . . 133 D.6 DiffuseSoundReflectionataBulkReactingPorousLayer . . . . . . . . 136 D.7 SoundReflectionandScatteringatFinite-SizeLocalAbsorbers . . . . . 136 D.8 Uneven,LocalAbsorberSurface. . . . . . . . . . . . . . . . . . . . . . . . 141 D.9 ScatteringattheBorderofanAbsorbentHalf-Plane . . . . . . . . . . . . 142 D.10 AbsorbentStripinaHardBaffleWall,withFarFieldDistribution. . . . 144 D.11 AbsorbentStripinaHardBaffleWall,asaVariationalProblem . . . . . 146 D.12 AbsorbentStripinaHardBaffleWall,withMathieuFunctions . . . . . 148 D.13 AbsorptionofFinite-SizeAbsorbers,asaProblemofRadiation . . . . . 153 D.14 AMonopoleLineSourceAboveanInfinite,PlaneAbsorber; IntegrationMethod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 D.15 AMonopoleLineSourceAboveanInfinite,PlaneAbsorber; withPrincipleofSuperposition . . . . . . . . . . . . . . . . . . . . . . . . 162 D.16 AMonopolePointSourceAboveaBulkReactingPlane, ExactForms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 D.17 AMonopolePointSourceAboveaLocallyReactingPlane, ExactForms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 D.18 AMonopolePointSourceAboveaLocallyReactingPlane, ExactSaddlePointIntegration . . . . . . . . . . . . . . . . . . . . . . . . 170 D.19 AMonopolePointSourceAboveaLocallyReactingPlane, Approximations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 D.20 AMonopolePointSourceAboveaBulkReactingPlane, Approximations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 E ScatteringofSound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 F.P.Mechel E.1 PlaneWaveScatteringatCylinders . . . . . . . . . . . . . . . . . . . . . . 185 E.2 PlaneWaveScatteringatCylindersandSpheres . . . . . . . . . . . . . . 188 E.3 MultipleScatteringatCylindersandSpheres . . . . . . . . . . . . . . . . 198 E.4 CylindricalWaveScatteringatCylinders. . . . . . . . . . . . . . . . . . . 199

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F. P. Mechel (Ed.) Formulas of Acoustics. Second Edition. With contributions by: M. L. Munjal, M. Vorl ¨ander, P. K ¨oltzsch, M. Ochmann, A. Cummings,.
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