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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
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