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ACOUSTIC POWi:i: LEVELS
251
equipment installed in these two houses would create hearing levels differing by only 3 decibels, a difference which is little more than just distinguishable to the ordinary ear.
Attempts have been made to make the optimum absorption for theatres the yardstick for power capacity of reproducing equipment possible to install with satisfactory results. From the relation between optimum reverberation time and volume of auditorium, it is possible to compute a curve connecting volume and most desirable amount of absorption. 12 Hence, curves 2 to 4 may be calculated to show a theoretical relation connecting powers to produce a level of 80 decibels in auditoriums of different volume, assuming optimum absorption and a threshold flux of 4 X Kh16 watts per square centimeter. From the curves, and what we have already reviewed concerning amplifiers, limits for size of theatres and capacity of reproducing equipment could be established.
VOLUME IN CUBIC FEET
Fig.
4. Estimated Acoustic Power in Decibels above .006 Waff as a Function o/ Volume Assuming Optimum Absorption.
Fig. 4 shows the required acoustic power in decibels above 0.006 watt plotted against a logarithmic scale of volume. The variables are considered logarithmically since loudness and sensation level are logarithmic functions of acoustic power. It is apparent that over the limited range in which we are interested the equation rather exactly expressing the graphed relation is:
An, = 8.1 log V — 32.2. (3)
The value of 8.1, as the slope, indicates that the power in watts will increase as V, in cubic feet, to the 0.81 power. Corresponding to this logarithmic expression is the following for the acoustic power in microwatts:
3.64 VO.f
(4)
From what we have previously established, it follows that the electrical must be about 8 decibels above, and the amplifier single frequency capacity some 13 decibels above the acoustic power.
12Wolf, S. K.: "Theatre Acoustics for Sound Reproduction," Journal Society Motion Picture Engineers, 14 (1930). No. 2, p. 151.