By Paul. E Sabine
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Of the sound n El once, c From a) units remain. (1 2, 3 . . reflected the twice-reflected TjlJ sound, there is -^-(1 a) c 2 ; and of the sound that has been F*l reflected (n Summing up Total energy 1) times, the the entire series, = El [1 + (1 - residue is c n" 1 . we have a) + (1 - a) 2 + (1 - (1 Note that a) (1 in the analysis given, we have tacitly - a) 3 a)"- 1 ] assumed REVERBERATION (THEORETICAL} 49 that the sound is emitted discontinuously in instantaneous puffs or quanta of El/c units each and that it is absorbed instantaneously and discontinuousiy at the two ends of the In Fig.
Points the sum of the potential to i^racoM. 2 . and kinetic energies is constant and equal kinetic as well as the average The average potential energy throughout the cycle is one-half the maxior j^wwM. 2 or Trra/M. 2 1 The total energy, kinetic and potential, of a vibrating particle equals J^mco 2 A 2 or mum . Wave Motion. Having considered the motion of the individual particle, us trace the propagation of this motion from particle to particle as a plane wave, that is, a wave in which all particles of the medium in any given plane at right angles Let to the direction of propagation have the same phase.
We no longer assume that the particle motion occurs in a single direction parallel to the axis of the tube. As a result, the simple distribution of nodes and loops in the one-dimensional case gives place to an intricate pattern of sound intensities, a pattern which may be radically altered by even slight changes in the position of reflecting surfaces in the room and of the source of sound. , for m in Eq. (22) is replaced by a trebly infinite series with the number of possible modes -of vibraThe simplest three-dimensional greatly increased.