Beat, Resonance and Doppler Effect - James Sy SL 275 Chapin 击败，共振和多普勒效应-杰姆斯SY SL 275查.ppt

Sound–BeatsSuperpositionleadstobeats–variationinloudness

ResonanceOccursinfixedmedialengthLDependsonboundaryconditionsOccursonlyforcertainfrequenciesforwhichanintegralnumberof?or?wavelengthsfitinmediumlengthLAffectedbypropagationspeedinmedium

BoundaryConditionsEndsofmediumareeitheranodeorantinodeDeterminedbytheconfigurationofthesystemStringedinstruments→bothendsarenodesWoodwinds,brass,organs→oneendisalwaysanantinode,theotherendcanbeeither

ProcedureIdentifyphysicalsituation(stringoraircolumn)Identifyboundaryconditions(nodesorantinodes)Ifthesameuse?wavelengthsIfdifferentuse?wavelengthsSketchwaveforms→determinehowmany?or?λfitinlengthLForeachallowedn,solveforλnDeterminepropagationspeedvUsev=fλtofindfn

HarmonicSeriesofStandingWavesonaVibratingStringBothendsarenodes(N)–use?λsSketchSolveforλnIfvnotknownuseSolveforfn

HarmonicSeriesofaPipeOpenatBothEndsBothendsareantinodes(A)–use?wavelengthsSketchSolveforλnIfvnotknownuseSolveforfn

HarmonicSeriesofaPipeOpenatOneEndOneendA,otherendN–use?wavelengthsSketchSolveforλnIfvnotknownuseSolveforfn

HarmonicsforSameEndsNotethatwhenendsarebothnodesorbothantinodes,n=1,2,3,4,…f2=2f1→2ndharmonicor1stovertonef3=3f1→3rdharmonicor2ndovertonef4=4f1→4thharmonicor3rdovertonef5=5f1→5thharmonicor4thovertoneAndsoon…fn=nf1

HarmonicsforDifferentEndsNotethatwhenoneendisNandtheotherisA,n=1,3,5,7,…f3=3f1→3rdharmonicor2ndovertonef5=5f1→5thharmonicor4thovertonef7=7f1→7thharmonicor6thovertonef9=9f1→9thharmonicor8thovertoneAndsoon…fn=nf1→onlyoddharmonicsareallowed

PropagationSpeedInastringvdependsonthetensionTandlinearmassdensityμlinInanaircolumnvdependsontemperatureT

SoundLevelsDecibelordBscaleI0isthethresholdofhea