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the variations in thickness of felt are taken as abscissas ; then draw through the points the best fitting curves and average the corresponding ordinates taken from the curves thus drawn; and with these average ordinates redraw both families of curves. The points shown on the diagram are of course the original results obtained experimentally. In general they fall pretty close to the curves, although at times, as in the points noted, they fall rather far to one side.
The following will serve to present the points of particular interest revealed by the family of curves in Figure 12, where the absorption by the several thicknesses is plotted against pitch for abscissas. It is to be observed that a single thickness scarcely absorbs the sound from the eight, four, and two foot organ pipes, C, 64, C, 128, and C, 256, and that its absorption increases rapidly for the next two octaves, after which it remains a constant. Two thicknesses absorb more about twice as much for the lower notes, the curve rising more rapidly, passing through a maximum between C4 512 and C: 1024, and then falling off for the higher notes. The same is true for greater thicknesses. All curves show a maximum, each succeeding one corresponding to a little lower note. The maximum for six thicknesses coincides pretty closely to C4 512. The absorption of the sound by felt may be ascribed to three causes, — porosity of structure, compression of the felt as a whole, and friction on the surface. The presence of the maximum must be ascribed to the second of these causes, the compression of the felt as a whole. As to the third of these three causes, it is best to consult the curves of the next figure.
The following facts are rendered particularly evident by the curves of Figure 13. For the tones emitted by the eight-foot organ pipe, Ci 64, the absorption of the sound is very nearly proportional to the thickness of the felt over the range tested, six thicknesses, 6.6 cm. The curves for notes of increasing pitch show increasing value for the coefficients of absorption. They all show that were the thickness of the felt sufficiently great, a limit would be approached, — a fact, of course, self-evident, - but for C1024 this thickness was reached within the range experimented on; and of course the same is true for all higher notes, C6 2048 and C, 4096. The higher the note, the less the thickness of felt necessary to produce a maximum effect. The curves of C64, C, 128, C3 256, and C4 512, if extended backward, wonld pass nearly through the origin. This indicates that for at least notes of so low a pitch the absorption of sound would be zero, or nearly zero, for zero thickness. Since zero thickness would leave surface effects, the argument leads to the conclusion that surface friction as an agent in the absorption of sound is of small importance. The curves plotted
FIGURE 13. The absorbing power of felt of different thicknesses. The data, Figure 12, is here plotted in a slightly different manner, – horizontally on plotted increasing thickness, - and the curves are for notes of different frequency at octave intervals in pitch. Thus plotted the curves show the necessary thickness of felt for practically maximum efficiency in absorbing sound of different pitch. These curves also show that for the lowest three notes surface friction is negligible, at least in comparison with the other factors. For the high notes one thickness of felt was too great for the curves to be conclusive in regard to this point. Cz (middle C) 256.
do not give any evidence in this respect in regard to the higher notes, C. 1024, C. 2048, and C, 4096.
It is of course evident that the above data do not by any means
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cover all the ground that should be covered. It is highly desirable that data should be accessible for glass surfaces, for glazed tile surfaces, for plastered and unplastered porous tile, for plaster on wood lath and plaster on wire lath, for rugs and carpets; but even with these data collected the job would be by no means completed. What is wanted is not merely the measurement of existing material and wall surfaces, but an investigation of all the possibilities. A concrete case will perhaps illustrate this. If the wall surface is to be of wood, there enter the questions as to what would be the effect of varying the material, – how ash differs from oak, and oak from walnut or pine or whitewood; what is the effect of variations in thickness; what the effect of panelling; what is the effect of the spacing of the furring on which the wood sheathing is fastened. If the wall is to be plaster on lath, there arises the question as to the difference between wood lath and wire lath, between the mortar that was formerly used and the wall of to-day, which is made of hard and impervious plaster. What is the effect of variations in thickness of the plaster? What is the effect of painting the plaster in oil or in water colors ? What is the effect of the depth of the air space behind the plaster? The recent efforts at fireproof construction have resulted in the use of harder and harder wall surfaces, and great reverberation in the room, and in many cases in poorer acoustics. Is it possible to devise a material which shall satisfy the conditions as to fireproof qualities and yet retain the excellence of some of the older but not fireproof rooms ? Or, if one turns to the interior furnishings, what type of chair is best, what form of cushions, or what form of upholstery? There are many forms of auditorium chairs and settees, and all these should be investigated if one proposes to apply exact calculation to the problem. These are some of the questions that have arisen. A little data have been obtained looking toward the answer to some of them. The difficulty in the way of the prosecution of such work is greater, however, than appears at first sight, the particular difficulties being of opportunity and of expense. It is difficult, for example, to find rooms whose walls are in large measure of glass, especially when one bears in mind that the room must be empty, that its other wall surfaces must be of a substance fully investigated, and that it must be in a location admitting of quiet work. Or, to investigate the effect of the different kinds of plaster and of the different methods of plastering, it is necessary to have a room, preferably an underground room, which can be lined and relined. The constant temperature room which is now available for the experiments is not a room suitable to that particular investigation, and for best results a special room should be constructed. More
over, the expense of plastering and replastering a room — and this process, to arrive at anything like a general solution of the problem, would have to be done a great many times - would be very great, and is at the present moment prohibitive. A little data along some of these lines have been secured, but not at all in final form. The work in the past has been largely of an analytical nature. Could the investigation take the form of constructive research, and lead to new methods and greater possibilities, it would be taking its more interesting form.
The above discussion has been solely with reference to the determination of the coefficient of absorption of sound. It is now proposed to discuss the question of the application of these coefficients to the calculation of reverberation. In the first series of papers, reverberation was defined with reference to C4 512 as the continuation of the sound in a room after the source had ceased, the initial intensity of the sound being one million times minimum audible intensity. It is debatable whether or not this definition should be extended without alteration to reverberation for other notes than C4 512. There is a good deal to be said both for and against its retention. The whole, bowever, hinges on the outcome of a physiological or psychological inquiry not yet in such shape as to lead to a final decision. The question is therefore held in abeyance, and for the time the definition is retained.
Retaining the definition, the reverberation for any pitch can be calculated by the formula
where V is the volume of the room, K is a constant depending on the initial intensity, and a is the total absorbing power of the walls and the contained material. K and V are the same for all pitch frequencies. K is .164 for an initial intensity 109 times minimum audible intensity. The only factor that varies with the pitch is a, which can be determined from the data given above.
In illustration, the curves in the accompanying Figure 14 give the reverberation in the large lecture room of the Jefferson Physical Laboratory. The upper curve defines the reverberation in the room when entirely empty; the lower curve defines this reverberation in the same room with an audience two thirds filling the room. The upper curve represents a condition which would be entirely impractical for speaking purposes; the lower curve represents a fairly satisfactory condition.
Curves expressing the reverberation in the large lecture room of the Jefferson Physical Laboratory with (lower curve) and without (upper curve) an audience. These curves express in seconds the duration of the residual sound in the room after the cessation of sources producing intensities 105 times minimum audible intensity for each note. The upper curve describes acoustical conditions which are very unsatisfactory, as the hall is to be used for speaking purposes. The lower curve describes acoustically satisfactory conditions. Cg (middle C) 256.