Steady-state sound field in enclosures

The classical normal-mode theory expresses the steady-state soundfield in an enclosure produced by a sound source as a series of normal modes ofvibration.Experimental facts are not often explained by this theory,and it wasconjectured that the normal-mode expression is not the complete solution ofthe wave equation in the enclosure,but only the reverberant part of it,and thereshould be an additional term representing the direct spherical radiation to makethe solution complete.The problem is examined by critically reviewing the de-rivation of the normal-mode expression,and by theoretical analysis of thesteady-state sound field in the room and experimental measurements therein.The conjecture is thus confirmed,and it is definitely shown that the sound fieldshould contain the direct wave as well as the standing waves(normal modes)formed by the confinement of the boundary surfaces.Relevant mathematicalexpressions are derived.