Frequency Distribution of Normal Modes

Abstract

The formula obtained by Maa for the frequency distribution of the normal modes for a rectangular enclosure has been verified by a more direct computation and extended to apply to a cylinder, a sphere, and to a number of derived shapes. In all cases it is found that the number of normal modes with frequencies less than v is given by 4•rVv•/3c•q-•rAv=/4c•q -..., where V is the volume and A the surface area of the enclosure. The application of this result is illustrated by a calculation of resonance response and rate of decay of sound in a cylinder.Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 129.174.21.5 On: Sun,

Modal density function and number of propagating modes in ducts

“…The quantity ao will be interpreted here as the limiting value of the eigenvalue for which sound propagation can occur. This idea of propagation involves the cut-off ratio defined as -777 (5) 1 _MI When equation (5) is used in equation (2), it is seen that at = 1 the radical in equation (2) vanishes and this will be termed cut-off. For < 1, the propagation coefficient 7 will be complex and damping occurs in the pressure (eq.…”