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Feb., 1930] LOUD SPEAKERS 167
-?......•;—•• : :<»
where
R = the average energy density.
PA = the acoustic power delivered by the sound source. c = the velocity of sound propagation. a = the summation of the products of the surface areas by their respective absorption coefficients.
From Sabine's reverberation equation the quantity a may be expressed in terms of the room volume V and the reverberation time T. Thus
aT = KV or
KV a = -f .-(2)
Substituting (2) in (1) and rearranging gives
KVcE V PA = —JTJT = K'E (3)
Theater observations with known values of PA and V and computed values for T (using Lifshitz' equation7) permitted an evaluation of K'E for sound intensities which were judged satisfactory for sound picture work. Assuming that the same energy densities are required for other theaters it is then possible by means of equation (3) to evaluate PA for a properly damped theater of any size. Fig. 2 shows the results of such computations. While this curve is based on observations in a number of theaters it has not been verified extensively and is presented here merely as an aid in the following discussion.
Small Theater Installation. — Consider now the case of a small theater. It has been found from surveys of a large number of sound picture theaters that the average size of the small theater (less than 100,000 cubic feet) is about 70,000 cubic feet with a seating capacity of about 650 people. Assuming this value of 70,000 cubic feet for purposes of discussion and referring to Fig. 2 it will be clear that the average small theater should have loud speakers capable of delivering an acoustic power of 0.46 watt. Such theaters will then require the
7 Physical Review (March, 1925).