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252 CINEMATOGRAPHIC ANNUAL
The premises of the theory leading to the above equation should be examined to obtain an accurate estimate of the conclusions reported in the preceding paragraph. The formula,
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expresses the average conditions existing when a sound source of constant power is in equilibrium with the absorption of energy at the surfaces enclosing a room. The average is to be understood as the total energy in the enclosed space divided by the volume. The condition of equilibrium means that a steady state must be reached before the equation holds true. It can be shown that the time necessary for conditions to approximate the steady state is something greater than 0.3 second for most theatres. In soeech the consonant portions of the syllables require only about 0.05 second for enunciation, the vowel sounds about 0.2 seconds.13 Therefore, application of the equation to obtain loudness produced by speech sounds is open to doubt as the times dealt with are rather too short for the assumptions to apply in all but the smaller volumes. Furthermore, the theory assumes random distribution while it is desirable to have sound reach the audience directly from the screen if illusion is to be maintained. Calculations have been made showing that loudness at pomts in an auditorium is affected less than 5 decibels bv helpful reflections.14 The impression of loudness is obtained mostly from direct energy, especially with directional sources such as horn speakers. Accordingly the absorption present cannot be correctly indicative of sensation level.
The formula obviously breaks down in the limiting case of open air theatres, or in enclosures where the surfaces are nearly 1 00 per cent absorbent as here a modified inverse square of distance relation applies. As wall surfaces are made more absorbing, the assumptions necessarv for tW derivation of rb^ formula are less annlirabK Several writers have advocated acoustically "dead" theatres.15 In this event, loudness, and consequently amplifier output to produce it, must be figured on some other basis as we shall see in the next section.
If we do not accept the absorption theory as a criterion, we must seek a new basis for a computation of the required acoustic power. Another starting point for the theoretical calculation would be the area occupied by an audience and presented to the horn to be covered. Thus, if uniform distribution could be achieved, a reproducing system with an arouse caoacitv of 200 milliwatts could nroduce a sensation level of 80 decibels over an area of 5400 square feet, neglecting any aid from reflection. The same system with proper distribution would produce a level of 77 decibels over twice the area, 10,800 square feet.
1?Crandall. I. B.: "Sounds of Speech. " Bell System Technical Journal, 4 (1925). No. 4. p. 586.
14Petzold, E.: "Elemcntare Raum Akustik." 1st Ed., Bauwelt-Verlag. Berlin (1927), p. 74.
15Kellogg, E. W. : "Some New Aspects of Reverberation," Journal Society Motion Pictu-e Engineers. 14, (1930). No. I, p. 9b. Watson. F. R.: "Acoustics of Buildings," 2nd Ed.. John Wiley and Sons. New York (1930), p. 58.