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Absorption of Sound by Materials I LLINOI S UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN PRODUCTION NOTE University of Illinois at Urbana-Champaign Library Large-scale Digitization Project, 2007. UNIVERSITY OF ILLINOIS BULLETIN ISSUED WEEKLY Vol. XXV November 29, 1927 No. 13 [Entered as second-class matter December 11, 1912, at the post office at Urbana, Illinois, under the Act of August 24, 1912. Acceptance for mailing at the special rate of postage provided for in section 1103, Act of October 3, 1917, authorized July 31, 1918.] THE ABSORPTION OF SOUND BY MATERIALS BY FLOYD R. WATSON PROFESSOR OF EXPERIMENTAL PHYSICS BULLETIN No. 172 ENGINEERING EXPERIMENT STATION P•UISHIB BY TB UNIVmrft bwILLIOIS, UWANA PnicE: TwMrTY 'GNTa ,yT HE Engineering Experiment Station was established by act of the Board of Trustees of the University of Illinois on December 8, 1903. It is the purpose of the Station to conduct investigations and make studies of importance to the engineering, manufacturing, railway, mining, and other industrial interests of the State. The management of the Engineering Experiment Station is vested in an Executive Staff composed of the Director and his Assistant, the Heads of the several Departments in the College of Engineering, and the Professor 6f Industrial Chemistry. This Staff is responsible for the establishment of general policies gov- erning the work of the Station, including the approval of material for publication. All members of the teaching staff of the College are encouraged to engage in scientific research, either directly or in eo5peration with the Research Corps composed of full-time research assistants, research graduate assistants, and special investigators& To render the desults of its scientific investigations available to the public, the Engineering Experiment Station publishes and distributes a series of bulletins. Occasionally it publishes circu- lars of timely interest, presenting information of importance, compiled from Various sources which may not readily be acces- sible to the clientele of the Station. The volume and number at the top of the front cover page are merely arbitrary numbers and refer to the general publica- tions of the University. Either above the title or below the seal is given the number of the Engineering Experiment Station bul- letin or circular which should be used in referring to these pub- lications. For copies of bulletins or circulars or for other information address THE ENGINEERING EXBERIMENT STATION,) UNIVERSITY OF ILLINOIS, URBANA, ILLINOIS ^ ** *. UNIVERSITY OF ILLINOIS ENGINEERING EXPERIMENT STATION BULLETIN No. 172 NOVEMBER, 1927 THE ABSORPTION OF SOUND BY MATERIALS A METHOD OF MEASUREMENT, WITH RESULTS FOR SOME MATERIALS BY FLOYD R. WATSON PROFESSOR OF EXPERIMENTAL PHYSICS ENGINEERING EXPERIMENT STATION PUBLISHED BY THE UNIVERSITY OF ILLINOIS, URBANA CONTENTS PAGE I. INTRODUCTION ... 5 1. Object of Investigation .. 5 2. Acknowledgments . 5 II. THEORY . 5 3. Definition of Acoustic Absorption . 5 4. Action of Sound in a Room . 5 5. Equation for Decay of Sound in a Room . 6 6. Application of Equation to Experimental Conditions . 7 7. Measurement of Sound Absorption by Instruments With- out Aid of the Ear . 10 8. Measurement of Sound Absorption by Means of Stand- ing Waves in a Tube . 13 9. Measurement of Intensity of Sound with Rayleigh Disc . 13 III. APPARATUS AND METHODS . 14 10. Outline of Method of Measurement . 14 11. Sources of Sound . 17 12. Reverberation Room .. 18 13. Rayleigh Disc and Its Use . 18 14. Sources of Error . .... 19 IV. EXPERIMENTAL RESULTS BY REVERBERATION METHOD . 20 15. Sound Absorption of Bare Room . 20 16. Sound Absorption of Open Windows . 21 17. Sound Absorption of Various Materials . 23 18. Table of Coefficients of Various Materials . 24 V. CONCLUSIONS ... 24 19. Conclusions . 24 LIST OF FIGURES NO. PAGE 1. Reflection, Absorption, and Transmission of Sound . 6 2. Curve Showing Decay of Sound in a Room . 8 3. Curve Showing Effect of Sound Absorbing Material in a Room . 9 4. View of Reverberation Room . 10 5. View of Tone Variators . 11 6. View of Audio Oscillator and Auxiliary Apparatus . 12 7. Diagram of Conne'ctions for Audible Frequency Oscillator . 13 8. View of Box Enclosing the Rayleigh Disc . 14 9. Diagram of Rayleigh Disc and Protecting Box . 15 10. Graph for Calculating Sound Absorption of Room . .. 16 LIST OF TABLES 1. Results for Reverberation in Bare Room . 20 2. Results for Sound Absorbing Units of Bare Room . 21 3. Sound Absorbing Coefficients for Open Windows . 23 4. Sound Absorbing Coefficients of Various Materials . 23 5. Sound Absorbing Coefficients for Range of Pitch . 25 6. Sound Absorbing Coefficients for Pitch 512. 26 THE ABSORPTION OF SOUND BY MATERIALS I. INTRODUCTION 1. Object of Investigation.-The increasing demand for quiet in buildings and auditoriums has stimulated the use and development of materials with sound-absorbing qualities. This movement has been at- tended with persistent inquiries about the sound-absorbing efficiencies of various products because the numerical coefficient of a material must be known to calculate the amount of it needed to adjust the acoustics of any room. The object of the investigation described in this bulletin was to determine experimentally the absorption coefficients for a num- ber of materials for the information of architects and others interested. The theory and method of measurement are described at some length. 2. Acknowledgments.-Acknowledgment is cheerfully given to members of the staff of the Physics Department for suggestions, and particularly to Prof. A. P. Carman for his encouragement. Prof. James M. White, the Supervising Architect, has given generous assistance in aiding the work. The investigation has been a part of the work of the Engineering Experiment Station of which Dean M. S. Ketchum is the director, and of the Department of Physics of which Prof. A. P. Carman is the head. II. THEORY 3. Definition of Acoustic Absorption.-Sound incident on a ma- terial is reflected, absorbed, and transmitted, as indicated in Fig. 1. When such a material is installed on the walls of a room, its absorbing effect includes the transmitted sound as well as the pure absorption in the material. In this sense an open window is considered a "perfect" absorber, but is really a perfect transmitter. The coefficients deter- mined are based on this conception; that is, that what is not reflected is "absorbed." The open window is taken as the standard absorber with a coefficient of 1.00, or 100 per cent absorption. A material in the room with a coefficient of absorption of 0.50, means that it absorbs 50 per cent as much sound as an open window of equal area. 4. Action of Sound in a Room.-Since the purpose of this investi- gation is to determine the absorption by materials installed on the walls of rooms, it is desirable to consider the action of sound under these conditions. Thus, if a sound is generated in a room it proceeds outwards in spherical waves from the source to the walls where it is ILLINOIS ENGINEERING EXPERIMENT STATION FIG. 1. REFLECTION, ABSORPTION, AND TRANSMISSION OF SOUND reflected, absorbed, and transmitted as shown in Fig. 1. The reflected sound then proceeds to a second wall where it is again reflected, ab- sorbed, and transmitted, and so on, experiencing from 200 to 300 re- flections for an average sound before its energy is all absorbed or transmitted. This means that with a steady sound, such as a sustained tone of an organ, each area of wall or a material on a wall, is sub- jected simultaneously to the combined action of a large number of sounds-the one striking it directly, the one striking it after one reflec- tion, the one after two reflections, and similarly for all the other sounds down to the one which is just dying out. In calculating the ab- sorption, it is necessary to develop an equation that takes account of this complex action. 5. Equation for Decay of Sound in a Room.-Thus, in accordance with the action of sound as described in Section 4, W. C. Sabine* de- veloped a reverberation equation which may be writtent -avt Ap _ avV where E = energy of sound per unit volume in a room at the time t A = rate of emission of energy from the source of sound p = mean free path of sound between reflections a = average coefficient of absorption v = velocity of sound V = volume of room t = time at any instant after the source of sound is stopped *Wallace C. Sabine. "Collected Papers on Acoustics," Harvard University Press, Cambridge, 1922. tF. Aigner. "Experimentelle Studie uiber den Nachhall," Sitz. Ber. der Wiener Akad., 2a Vol. 123, pp. 1489-1523, 1914. THE ABSORPTION OF SOUND BY MATERIALS Sabine conducted an extended series of fundamental experiments that justified his theory. Other forms of the equation have been developed by Franklin,* Jdger,t Buckingham,f and Eckhardt.I Jdger's equation, which is convenient for use, is 4 -avst k t E = Ee- 4A 4' avs where the quantities are the same as noted in Sabine's equation, ex- cept that s - total area of surfaces exposed to the sound waves, so that 4V p - -, and p is replaced by the more easily accessible quantities, V S and s. Solving equation (1) for t gives 4V2.3 4A V 4A t - log o 4 - constant - log 4A avs 10 avsE as 10 avsE or, in words, reverberationvolume X loudness time of reverberation c. absorption since the loudness is proportional to the logarithm of the intensity log - . Experimentally, the problem is to determine the absorp- avsE/ tion a. For convenience, the factors as are abbreviated to a, and E is given the arbitrary value of unity ("threshold intensity," see Fig. 2), so that t 4V2.3 l 4A t -- go -- av av The value of A is thus fixed in the same units as those for which E = 1.
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