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Vibrations of the Air in a Chamber.
markable difference in the apparent direction of the sound in different positions of the ear with respect to
a. Suppose that, being provided with the apparatus just described, we shut ourselves up in an apartment of regular figure, and free from furniture or projections from the walls, recesses, &c., and place one of our resonant cylinders with its axis horizontal, and the vibrating bell or glass opposite its orifice. In the direction of its axis place the membrane horizontally, with its proper frame and resonant cylinder below it, and strew the horizontal surface with sand.
If now, first, we place the membrane thus armed very near the source of the sound, it will vibrate with great force. As we withdraw it, (keeping it still in the line of the axis of the first resonant cylinder,) its vibrations will diminish gradually, and at length cease; after which, (still continuing to remove it along this line,) they will recommence and reach a maximum, at a point where their intensity is nearly equal to that close to the source of sound. Removing the membrane yet further, a new point of indifference is found, and so on till we reach the end of the chamber.
b. If we walk along the same line, keeping the ear in the plane of the horizontal axis of the resonant cylinder, we shall perceive the sounds to be much louder in the places where the vibrations of the membranes attain their maxima, than at the intermediate points where they are at their minima, and where the sounds would almost disappear, if it were not for the condensations and rarefactions of the air, which are there at their maxima.
c. At these latter a very curious phenomenon has been observed by M. Savart. When the auditor moves his head away from such a point, towards the right, (always supposing it to remain in the line of the axis above mentioned,) the sound will appear to come from the right, and if towards the left, it will seem to come from the left, whether the original source of sound be to the one or other side. This singular effect shows that the aerial molecules, on
Spiral Form of the Nodal Lines in a Rectangular Chamber.
either side of the point of indifference, are in opposite states of motion at any given instant. In making this experiment, the head should be so turned, that the axis of the resonant cylinder prolonged shall pass through both ears. Suppose, for instance, the sounding apparatus to be to the observer's left, and that his head be very near it. The sound will appear to enter at his left ear. As he removes farther away, so as to pass one of the nodes, it will seem as if the sound had changed sides, and now came from the right. When another node is passed, it will appear to have again shifted to the left, and so on.
d. But if we quit the axis of the cylinder, and carry an exploring membrane, such as already described, about the apartment, noting all the points where it vibrates most forcibly, allowing ourselves, as it were, to be led from spot to spot by its indications, we shall trace out in the air of the room a curve of double curvature, marking the maxima of the excursions of the aerial molecules.
If the experiment be made in a gallery, or passage, whose length is its principal dimension, this curve will be found to be a kind of spiral, creeping round the walls, floor, and ceiling, obliquely to the axis of the gallery, thus presenting a marked analogy to the disposition of the nodal lines in a long rod vibrating tangentially; which are also, it should be remarked, imitated, with modifications more or less complicated, in square or rectangular rods.
e. A still more remarkable effect was observed by M. Savart, in thus exploring the vibrations of the air in an apartment with an open window. The spiral disposition of the vibrating portions was found to be continued out of the window into the open air, the lines of greatest intensity running out in great convolutions, which seemed to grow wider, on receding from the window, and could be traced to a great distance from it.
156. The vibrations of a column of air contained in a pipe may also be examined by means of these membranes, and the positions of the nodes will be
Vibrations of Air in Pipes Explored by Membranes.
found to be nearly as in art. 80, though they are somewhat affected by the embouchure, as might, in some degree, have been anticipated from the remarks of art. 85.
a. The vibrations of the air in an organ-pipe were explored by M. Savart, by lowering into the pipe, placed vertically with its upper end open, a thin membrane stretched on a light ring, and suspended by a fine silk thread, and strewed with sand. Thus ocular demonstration of the existence of its subdivision into distinct ventral segments was obtained, the sand remaining undisturbed when the membrane occupied precisely the place of a node.
b. By this means, too, the influence of the embouchure on the places of the nodes, a curious and delicate point in the theory of pipes may be subjected to exact examination. Thus, for instance, when the column of air in the pipe vibrates in the manner described in art. 79, (fig. 19,) having two half ventral segments, and one node in the middle, it is found that the node is only approximately so placed, being always, in fact, nearer to the embouchure than to the open end.
157. It is well known that, if we sing near the aperture of a wide-mouthed vessel, some one note (which is in unison with the air in the vessel) will be reinforced and augmented, and sometimes to a great degree. This is what is meant by the resonance of the mass of air contained in the cavity of the vessel, or as it may be termed, the resonance of the cavity.
a. This has been known from the earliest times. The ancients are said to have placed large brass jars under the seats of their immense theatres to reinforce (one does not well see how) the voices of the actors.
b. Any vessel or cavity may be made to resound by placing opposite its orifice a vibrating body, having a surface large enough
Resonance of Cavities.
to cover the aperture, or at least to set a considerable portion of the aerial stratum adjacent to it in regular oscillation, and, at the same time, pitched in unison with the note which the cavity would of itself yield.
The experiment of the disked tuning-fork, in art. 93, is a case exactly in point. The pipe, which resounds in that experiment, may be pitched exactly in unison with it by its stopper, and in proportion as it departs from a perfect unison the resonance is feebler.
A series of disked tuning-forks, or vibrating steel springs, thus placed over the orifices of pipes carefully tuned, constitutes a very pretty musical instrument, capable of a fine swell and fall, according as the discs are brought nearer to, or further from, the orifices of the pipes, or inclined to their axes, and of remarkable purity and sweetness of tone.
A similar adaptation of resonant cavities to a series of harmonica glasses, fixed on a common revolving axis, has been recommended by M. Savart as the principle of a musical instrument, whose effect, should it be found to answer the expectations, which his description of the tones thus drawn forth is calculated to excite, would probably surpass that of all others yet invented. The cavities best adapted to this purpose are short cylinders of large diameters, with movable bottoms fitting by tight friction by which they may be tuned.
158. Such cavities may be regarded as short organpipes. When the diameter of a pipe is greatly increased in proportion to its length, so that it becomes a box, the law of the proportionality of the time of vibration to the length ceases to hold good, and the note yielded is flatter than that of a narrow pipe of equal length, and the more so the wider the pipe.
a. Thus M. Savart found that a cylinder of 4 inches in length, and 5 in diameter, resounded in unison with a narrow pipe 6 inches long, making 1024 vibrations per second
Resonance and Vibrations of Box-Shaped Cavities.
b. That sagacious experimenter has found, that cubical boxes speak with surprising promptitude and facility, and yield sounds extremely pure, and of a peculiar quality; on which account, and by reason of the little height in which they may be packed, he recommends them for organ-pipes. A cube of 4 inches in the side yields the same note as a pipe 10 or 11 inches long, and 2 or 21 inches in diameter.
They may be excited by an embouchure at one edges, precisely similar to that of an organ-pipe. also speak if the embouchure be situated in the
of their lower But they will middle of the
c. M. Savart has also examined the vibrations of a great variety of different shaped pipes, boxes, or cavities.
159. There is yet another remarkable case of vibrations, communicated between the different members of a system, of which we have not yet spoken, though offering a good example of the verification of the general law of equality of period and parallelism of direction of the vibratory motions of all the molecules of a system laid down in art. 151. It is when vibrations are communicated through a liquid.
The following experiments of M. Savart will show the mode in which this is accomplished.
a. He took a cylindrical tinned iron vessel whose bottom was placed parallel to the horizon, and having cemented to its centre a glass rod, so as to hang perpendicularly down from it, he covered the bottom to the depth of about an inch and a half with water, on which was floated a thin disc of varnished wood, covered on its upper face with sand.
The apparatus thus prepared, he impressed on the glass rod a longitudino-tangential vibration, which of course became normal when communicated to the bottom of the vessel; and he observed the sand on the upper face of the disc to be agitated with normal