THE SCIENCE AND APPLICATIONS OF ACOUSTICS - H. H. Arnold ...

11.13 Sound Levels due to Direct and Reverberant Fields 259one reflection:Power supplied = W (1 − α)The steady-state condition results inc DR Sα= W (1 − α)4which we rearrange to obtain the energy density in the reverberant field,DR = 4W 1 − ααcSwhere the room constant R is by definition= 4WcR(11.21)R =αS1 − α .In most cases, the boundaries of the actual enclosure and other objects inside theenclosure are constructed of different materials with differing absorption coefficients.The room constant R of the enclosure is then described in terms of meanproperties byR = ST α1 − αwhereR = the room constant (m 2 )S T = total surface area of the room (m 2 )ᾱ = mean sound absorption coefficient = ∑ α i S i /S T .11.13 Sound Levels due to Direct and Reverberant FieldsNear a point of nondirectional sound source, the sound intensity is greater thanfrom afar. If the source is sufficiently small and the room not too reverberant,the acoustic field very near the source is independent of the properties of theroom. In other words, if a listener’s ear is only a few centimeters away from aspeaker’s mouth, the room surrounding the two persons has negligible effect onwhat the listener hears directly from the speaker’s mouth. At greater distancesfrom the source, however, the direct sound decreases in intensity, and, eventuallythe reverberant sound predominates.If we are more than one-third wavelength from the center of a point source, theenergy density of a point r is given by Equation (11.20) for the direct sound field.Combining the Equations for the direct and the reverberant sound intensities, i.e.,Equations (11.20) and (11.21), we get the total sound intensity I given by[ Q(θ,φ)I = W + 4 ](11.22)4π r 2 R