Inthenormal-modetheoryofMorse,itgivesaseriesofnormalmodesasthesolutionofforcedvibrationinaroom.Butactuallythereisalwaysthedirectradiationbesidesthenormalmodeswhichrepresentthereverbrantsoundfieldonly.Thereasonisthatthenormalmodeswereassumedonlyinthesource,andnaturallynormalmodesonlyareobtainedinthesolution.Atheoryofdoublesourceisproposed,thatthesoundsourceisboththesourceofthedirectradiationasifinfreespacebeforetheboundarysurfaceswerereachedbythedirectradiation,andafterthefirstreflectionfromtheboundarysurfaces,thesourceofthereflectedwavelets,randomlydistributedbothinspaceanintimeontheboundarysurfacesthatbuildupthenormalmodesafterfurtherreflections.Thewaveequationisformedaccordingly,andthesolutionofthewaveequation,thesoundfieldinaroom,containsexplicitlyboththedirectradiationandthereverberantsoundformedofnormalmodes.Theapproximatemeansquaresoundpressureisfoundtobethedircetsounddeterminedbythesoundpowerofthesource,andreverberantsounddeterminedbythesoundpowerreducedbyafactorofπ/2,differentslightlyfromtheresultobtainedfromenergyconsideration,ifthesourceispuretone.Thereisessentiallynodifferenceforasourceofbandnoise.
