By Paul. E Sabine
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Extra resources for Acoustics And Architecture
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.
The horizontal component the of the piston of the uniform circular motion of the disk is transmitted to the piston by the pin, which slides up and down in the vertical slot in the piston head as the disk revolves. We may consider that the disturbance is kept from spreading 1 The mathematical proof of this statement is not difficult. The interested reader with an elementary knowledge of the calculus may easily derive the proof for himself. ACOUSTICS AND ARCHITECTURE 16 laterally by having in a tube so long that the medium propagating we need not consider confined what happens at the open end.
Referring to Eq. absorbent barrier ? (d+r) \(l - 18, = A[sin k) sin wt cos -2fc A cos At the write in the case of an - k sin art c sin intcrnodes, cos J 5) co(< L = we may ^ c (1 + co(* + -tA(l k) cos - is zero, *>* = c amplitude is A (1 k). 1, and - u(t sin (23o) - -} = c at these points the displacement amplitude while at the nodes cos 1 c J *) sin and sin is = sin c 1; A(l 0, (236) hence + k} t and the SUSTAINED SOUND IN AN INCLOSURE 39 We note from the form of Eq. (236) that the particle displacement due to the direct and reflected waves represents a progressive wave of amplitude A (I k) superimposed upon a stationary wave of amplitude 2kA.
Acoustics And Architecture by Paul. E Sabine