paul e sabine acoustics and architecture doc

03 OU 158930 >m [...]... the departure from the law is quite as marked Figure 2 gives the results of measurements made in a large armory with the Webster phonometer using an organ pipe blown at constant pressure as the source Here the heavy curve gives what the phonometer readings would have been on the assumption of an intensity decreasing as the square of the distance increases The measured values are shown on the broken... it alone were sufficient As examples of remedies may be cited the placing of vases about the room for the sake of resonance, wrongly supposed to have been the object of the vases in Greek theaters, and the stretching of wires, even now a frequent though useless device in 1 SABINE, WALLACE University Press, p 1 C., "Collected Papers on Cambridge 1922 Acoustics, " Harvard INTRODUCTION 11 In a succeeding... complete , P ACOUSTICS AND ARCHITECTURE 20 F A wave length period, there is again a condensation at therefore as defined above includes one complete condensation and one rarefaction of the medium - The condensation, denoted by the letter s, is defined as the ratio of the increment of density to the undisturbed density: -* P Thus if the density of the undisturbed air is 1.293 g: per and that in the condensation... motion and the development of the wave equation in Chap II would be much vi PREFACE more neatly handled for the mathematical reader by the use of the differential equation of the motion of a particle under the action of an elastic force The only excuse for the treatment given is the hope that it may help the non- mathematical reader to visualize more clearly the dynamic properties of a wave and its propagation... dynes per square centimeter; and by the Newton formula the value of c should be c = = Vqipni'ooQ 27,990 cm./sec = 918.0 ft./sec The experimentally determined value of c is about 18 per cent greater than this theoretical value given by the Newton formula This disagreement between theoTy and experiment was explained in 1816, by Laplace, who pointed out that the condition of constant temperature under... we assume a source of sound of small area set up in the open air away from all reflecting surfaces, we should expect the energy to spread in spherical waves with the source of sound as the center At a distance r from the source, the total energy from the source passes through free E 2 If the surface of a sphere of radius r, a total area of 4?rr is the energy generated per second at the source, then... the wave length, or the velocity of sound if the two other quantities are known Since c, the velocity of sound in air at any temperature, is known, the wave length of sound of any given freI of Appendix A gives the frequencies and wave lengths in air at 20 C (68 F.) of the tones of one octave of the tempered and physical scales The frequencies and wave lengths given are for the first octave above middle... should one measure the length to the back or to the Few front of the galleries, to the back or front of the stage recess? rooms have a flat roof where should the height be measured? One writer, who had seen the Mormon Temple, recommended that all : auditoriums be Sanders Theater is by far the best auditorium elliptical Cambridge and is semicircular in general shape but with a recess that makes it almost... of the better known measurements of the velocity of sound INTRODUCTION Other determinations have been made, all in close agreement with the values shown in Table I, so that it may be said that the velocity of sound in free atmosphere is known with a fairly high degree of accuracy The weight of all the experimental evidence is to the effect that this velocity is independent of the pitch, quality, and. .. scientific papers on the subject On the architectural side, we find numerous references to the subject, beginning with the classic work on archiIn these tecture by Vitruvius ("De Architectural- ACOUSTICS AND ARCHITECTURE 10 we references, on more or find, for the most based part, only opinion, less superficial observation Nowhere there evidence either of a thoroughgoing analysis of the problem is any attempt . the wave equation in Chap. II would be much vi PREFACE more neatly handled for the mathematical reader by the use of the differential equation of the motion of a particle under the action of an elastic force. The only excuse for the treatment given is the hope that it may help the. more adequate appreciation of the precision of the solution reached. No attempt has been made to present a full account of all the researches that have been made in this field in very recent years. Valuable contributions to our. of gas be suddenly compressed, its temperature rises. This rise of temperature makes necessary a greater pressure to produce a given volume reduction than is necessary if the compression takes place slowly,