Popular Science Monthly/Volume 14/November 1878/Experiments in Sound
SOUND is the sensation peculiar to the ear. This sensation is caused by rapidly-succeeding to-and-fro motions of the air which touches the outside surface of the drum-skin of the ear. These to-and-fro motions may be given to the air by a distant body, like a string of a violin. The string moves to and fro, that is, it vibrates. These vibrations of the string act on the bridge of the violin, which rests on the belly or sounding-board of the instrument. The surface of the sounding-board is thus set trembling, and these tremors, or vibrations, spread through the air in all directions around the instrument, somewhat in the manner that water-waves spread around the place where a stone has been dropped into a quiet pond. These tremors of the air, however, are not sound, but the cause of sound. Sound, as we have said, is a sensation; but, as the cause of this sensation is always vibration, we call those vibrations which give this sensation sonorous vibrations. Thus, if we examine attentively the vibrating string of the violin, we shall see that it looks like a shadowy spindle, showing that the string swings quickly to and fro; but, on closing the ears, the sensation of sound disappears, and there remains to us only the sight of the quick to-and-fro motion which the moment before caused the sound.
Behind the drum-skin of the ear is a jointed chain of three little bones. The one, H in Fig. 4, attached to the drum-skin, is called the hammer; the next. A, is called the anvil; the third, S, has the exact form of a stirrup, and is called the stirrup-bone. This last bone of the chain is attached to an oval membrane, which is a little larger than the foot of the stirrup. This oval membrane closes a hole opening into the cavity forming the inner ear; a cavity tunneled out of the hardest bone of the head, and having a very complex form. The oval hole just spoken of opens into a globular portion of the cavity, known as the vestibule; and from this lead three semicircular canals, SC, and also a cavity, C, of such a marked resemblance to a snail's shell that it is called cochlea, the Latin word for that object. The cavity of the inner ear is filled with a liquid, in which spread out the delicate fibres of the auditory nerve.
Let us consider how this wonderful little instrument acts when sonorous vibrations reach it. Imagine the violin-string vibrating 500 times in one second. The sounding-board also makes 500 vibrations in a second. The air touching the violin is set trembling with 500 tremors a second, and these tremors speed with a velocity of 1,100 feet in a second in all directions through the surrounding air. They soon reach the drum-skin of the ear. The latter, being elastic, moves in and out with the air which touches it. Then this membrane, in its turn, pushes and pulls the little ear-bones 500 times in a second. The last bone, the little stirrup, finally receives the vibrations sent from the
violin-string, and sends them into the fluid of the inner ear, where they shake the fibres of the auditory nerve 500 times in a second. These tremors of the nerve—how we know not—so affect the brain that we have the sensation which we call sound.
In Chapter V. it is shown that the mechanical actions, which finally result in giving us the sensation of sound, always have their origin in some vibrating body, and that this vibrating body may be either solid, liquid, or gaseous. The author, after showing that the vibrations of a solid (a tuning-fork) and of a liquid (water running through a toy flageolet) give origin to sound, presents to his readers—
An Experiment made with a Whistle and a Lamp-Chimney, showing that, as in Wind-Instruments, a Vibrating Column of Air may originate Sonorous Vibrations.—Experiment 33.—The chimneys of student-lamps have a fashion of breaking just at the thin, narrow part near the bottom. Such a broken chimney is very useful in our experiments. At A, in Fig. 25, is such a broken chimney, closed at the broken end with wax. A cork is fitted to the other end of the chimney, and has a hole bored through its centre. In this hole is inserted part of a common wooden whistle. At B is an exact representation of such a whistle, and the cross-line at C shows where it is to be cut in two. Only the upper part is used, and this is tightly fitted into the cork.
Inside the tube is a small quantity of very fine precipitated silica, probably the lightest powder known. Hold the tube in an horizontal position and blow the whistle. The silica-powder springs up into groups of thin vertical plates, separated by spots of powder at rest, as in the figure. This is a very beautiful and striking experiment.
Experiment 33 a.—The following experiment shows that the sound is caused by the vibrations of the column of air in the tube and whistle, and not by the vibrations of these solid bodies. Grasp the tube and whistle tightly in the hands. These bodies are thus prevented from vibrating, yet the sound remains the same.
The breath driven through the mouth of the whistle strikes on the sharp edge of the opening at the side of the whistle, and sets up a flutter or vibration of air. The air within the glass tube now takes part in the vibrations, the light silica-powder vibrates with it, and makes the vibrations visible.
To exhibit this experiment before a number of people, lay the tube carefully on the water-lantern before the heliostat, and throw a projection of the tube and the powder on the screen. When the whistle is sounded, all in the room can see the fine powder leaping up in the tube into thin, upright plates.
From Chapter VI., which is on the transmission of sonorous vibrations through solids, liquids, and gases, we select—
Experiments showing that the Air is constantly vibrating while Sonorous Vibrations are passing through it.—We must now add to our apparatus an open metal A pipe about seven and a half inches (nineteen centimetres) long, shown at C in Fig. 27. This pipe the organ-builder will accurately tune to your "A-philharmonic" fork.
Experiment 43.—Get a glass tumbler about two and a half inches in diameter and about three and a half inches deep, though any tumbler will do. Take a piece of window-glass about three inches square and place it over the tumbler. The glass must touch the edge of the mouth of the tumbler all around. Now slowly slide the glass so that the opening into the tumbler gets larger and larger, while the vibrating fork is held all the time over this opening, as shown at A in Fig, 27. Presently you will get an opening of a size that causes an intense sound, much louder than any you have ever before heard from the fork alone. This is because the air in the tumbler is set in vibration, and adds the vibrations of its mass to those of the fork. That this is so you may prove for yourself by the following experiment:
Experiment 44.—Being careful not to move the glass plate from its present position (Experiment 43), stick it with wax to the tumbler. Pour a little silica into the tumbler, and then hold it horizontally, and vibrate the fork near its opening, observing attentively how the silica-powder is acted on by the inclosed vibrating air.
Experiment 45.—Take a piece of thin linen paper about four and a half inches square, and having wetted it paste it over the mouth of the tumbler. When the paper has dried it will be stretched tightly. Take a sharp penknife and carefully cut away the paper so as to make an opening as shown at B in Fig. 27. Make this opening small at first, and very gradually make it larger and larger. Hold the fork over the opening after each increase in its size, and you will soon discover the size of the opening which causes the air inclosed in the tumbler to vibrate with the fork, and thus greatly to strengthen its sound. You have now a mass of air in tune with the fork, and inclosed in a vessel which has one of its walls formed of a piece of elastic paper. With this instrument, which I have invented for you, you must make some charming experiments.
Experiment 46.—If the air in the tumbler vibrates to the A-fork, it will, of course, vibrate to the A-pipe, which gives the same note as the fork. Scatter some sand on the paper, and then sound the A-pipe a foot or two from it. The sand dances vigorously about, and ends by arranging itself in a nodal line parallel to the edges of the paper, in the form of a U with its two horns united by a straight line. The vibrations of the pipe can only reach the tumbler by going through the air, and, as the sand vibrates when the tumbler is placed in any position about the pipe, it follows that the air all around the pipe vibrates while the pipe is sounding.
Experiment 47.—Sprinkle a small quantity of sand on the paper, and then, placing a thin book under the tumbler, so incline it that the sand just does not run down the paper, as shown in B, Fig. 27. Now go to the farthest end of the room and blow the pipe in gentle toots, each about one second long. At each toot, your friend, standing near the tumbler, will see the sand make a short march down the paper; and soon by a series of marches it makes its way to the edge of the paper and falls into the tumbler, I have, in a large room, gone to the distance of sixty feet (18.28 metres), and the experiment worked as I have just described it.
Experiment 48.—Again arrange the experiment as in Experiment 47, and standing three or four feet from the tumbler try how feeble a sound will vibrate the paper. If every part of the experiment is in good adjustment, you will find that the feeblest toot you can make will set the sand marching. To keep it at rest you must keep silent.
Experiment 49.—To show these experiments on a greatly magnified scale, place the tumbler in front of the heliostat (see "Light," page 79) so that the sun's rays just graze along the inclined surface of the paper. Cut off a piece of a match one-eighth of an inch long, and split this little bit into four parts. Place one of these on the inclined paper. Of course, the image of the tumbler is inverted, so the bit of wood appears to adhere to the lower side of the paper. If a little paper mouse cut out of smooth paper is used in place of the bit of wood, it is really amusing to see the mouse make a start at every toot of the pipe.
We make a long selection from Chapter VIII., which treats of the "Interferences of Sonorous Vibrations, and of the Beats of Sound," in order to set forth the manner in which the author has knit together his simple experiments.
Experiment 60.—Cut out two small triangles of copper-foil or tinsel, of the same size, and with wax fasten one on the end of each of the prongs of a tuning-fork. Put the fork in the wooden block, and set up the guide (as in experiment, Fig. 21). Prepare a strip of smoked glass, and then make the fork vibrate and slide the glass under it, and get two traces, one from each prong.
Holding the glass up to the light, you will see the double trace, as shown in Fig. 37. You observe that the wavy lines move apart, and
then draw together. This shows us that the two prongs, in vibrating, do not move in the same direction at the same time, but always in opposite directions. They swing toward each other, then away from each other.
Experiment 61.—What is the effect of this movement of the prongs of the fork on the air? A simple experiment will answer this question.
Place three lighted candles on the table at A, B, and C (Fig. 38). Hold the hands upright, with the space between the palms opposite A, while the backs of the hands face the candles B and C. Now move the hands near each other, then separate them, and make these motions steadily and not too quickly. You thus repeat the motions of the prongs of the fork.
While vibrating the hands, observe attentively the flames of the candles. When the hands are coming nearer each other, the air is forced out from between them, and a puff of air is driven against the flame A as is shown by its bending away from the hands. But, during the above movement, the backs of the hands have drawn the flames toward them, as shown in Fig. 38. When the hands are separating, the air rushes in between them, and the flame A is drawn toward the hands by this motion of the air, while at the same time the flames at B and C are driven away from the backs of the hands. From this experiment it is seen that the space between the prongs and the faces of the prongs of a fork are, at the same instant, always acting oppositely on the air.
This will be made clearer by the study of the diagram, Fig. 39.
This figure supposes the student looking down on the tops of the prongs of the fork. Imagine the prongs swinging away from each other in their vibration. Then the action of the faces c and c on the air is to condense it, and this condensation tends to spread all around the fork. But, by the same movement, the space r r between the prongs is enlarged, and hence a rarefaction is made there. This rarefaction also spreads all around the fork. But, as the condensations produced at c and c and the rarefactions at r and r spread with the
same velocity, it follows that they must meet along the dotted lines q, q, q, q, drawn from the edges of the fork outward. The full 4-circle lines around the fork in Fig. 39 represent the middle of the condensed shells of air, while the broken 4-circle lines stand for the middle of the rarefied shells of air.
Now what must happen along these dotted lines, or, rather, surfaces? Evidently there is a struggle here between the condensations and the rarefactions. The former tend to make the molecules of air go nearer together, the latter try to separate them; but, as these actions are equal, and as the air is pulled in opposite directions at the same time, it remains at rest—does not vibrate. Therefore, along the surfaces q, q, q, q, there is silence. When the prongs vibrate toward each other they make the reverse actions on the air; that is, rarefactions are now sent out from c and c, while condensations are sent from r and r, but the same effect of silence along q, q, q, q, is produced.
Experiment 62.—That this is so, is readily proved by the following simple experiment: Vibrate the fork and hold it upright near the ear. Now slowly turn it round. During one revolution of the fork on its foot, you will perceive that the sound goes through four changes. Four times it was loud, and four times it was almost if not quite gone. Twirl the fork before the ear of a companion: he will tell you when it makes the loudest sound, and when it becomes silent. You will find that when it is loudest the faces c, c of the prongs, or the spaces r, r between them, are facing his ear; and when he tells you that there is silence you will find that the edges of the fork, that is, the planes q, q, q, q, are toward his ear.
Our space will only permit one more selection, and this we take from Chapter XVII., "On the Analysis and. Synthesis of Sounds," in order specially to show how Prof. Mayer has placed within the reach of all teachers and students an instrument giving some of the most charming experiments in acoustics. The whole apparatus, if made at home, need not cost over seventy-five cents.
Experiments by which Compound Sounds are analyzed by viewing in a Rotating Mirror the Vibrations of König's Manometric Flames.—Take a piece of pine board. A, Fig. 51, 1 inch (25 millimetres)
thick, 12 inch (38 millimetres) wide, and 9 inches (22.8 centimetres) long. One inch from its top bore with an inch centre-bit a shallow hole 8 inch deep. Bore a like shallow hole in the block B, which is 4 inch thick, 12 inch wide, and 2 inches (51 millimetres) long. Place a 2-inch centre-bit in the centre of the shallow hole in A and bore with it a hole through the wood. Into this fit a glass or metal tube, as shown at E. Bore a 16-inch (5 millimetres) hole obliquely into the shallow hole in B, and into this fit the glass tube C. Then bore another 16-inch hole directly into the shallow hole in B. Put a glass tube in a gas or spirit flame and heat it red-hot at a place about two inches from its end. Then draw the tube out at this place into a narrow neck. Make a cut with the edge of a file across this narrow neck, and the tube will readily snap asunder at this mark. Then heat a place on the tube in a flame, and here bend it into a right angle, as shown at D, Fig. 51. Now fit this tube into the hole just made, as shown at D. These tubes may be firmly and tightly fitted by wrapping their ends with paper coated with glue before they are forced into their holes.
Get a small piece of the thinnest sheet rubber you can find, or a piece of thin linen paper, and, having rubbed glue on the board A around the shallow hole, stretch the thin rubber, or paper, over this hole and glue it there. Then rub glue on the block B, and place the shallow hole in this block directly over the shallow hole in A, and fasten B to A by wrapping twine around these blocks. Thus you will have made a little box divided into two compartments by a partition of thin rubber. Fasten the rod A to the side of a small board, so that it may stand upright.
Attach a piece of large-sized rubber tube to the glass tube E, and into the other end of the tube stick a cone, made by rolling up a piece of cardboard so as to form a cone eight inches long and with a mouth two inches (51 millimetres) in diameter.
Now get a piece of wood one foot long, four inches wide, and a quarter of an inch thick. Out of this cut the square, with the two rods projecting from it, as shown at M. The lower of these rods is short, the one above the square is long. Cut the end of the shorter rod to a blunt point, and with this point make a very shallow pit in the piece of flat wood K for the rod and square to twirl in. Glue the piece of wood K on the end of a brick, L. Get two pieces of thin silvered glass, each four inches square, and, placing one on each side of the square M, fasten them there by winding twine around the top and bottom borders of the mirrors.
Experiment 112.—Through a rubber tube lead gas to C. It will go into the left-hand partition of the box and will come out at F, where you will light it. Now place the mirror-rod in the shallow pit in K, and hold the mirror upright, so that you may see the flame F reflected from its centre.
Hold the rod upright and twirl it slowly between the thumb and forefinger, which should point downward and not horizontally, as shown in the figure. The flame appears in the mirror drawn out into a band of light with a smooth top-border. While twirling the mirror put the cone to your mouth and sing into it. The sonorous vibrations enter the side A of the box, and, striking on the thin rubber, force this in and out. When it goes in, a puff of gas is driven out of the other partition, B, of the box, and the flame F jumps up. When the sheet of rubber vibrates outward, it sucks the gas into the box B, and the flame F jumps down. Therefore, on singing into the funnel, you will see in the mirror the smooth top-border of the luminous band broken up into little tongues or teeth of flame, each tooth standing for one vibration of the voice on the rubber partition.
Place a lamp-chimney around the flame, should the wind from the twirling mirror agitate it, and be careful not to have the flame too high.
Experiment 113.—Another way of showing the vibrations of the flame is to burn the jet of gas at the end of a glass tube stuck into the end of a rubber tube attached to F. Now sling the tube round in a vertical circle, and you have an unbroken luminous ring; but as soon as you sing into the cone this ring breaks up into a circle of beads of light, or sometimes changes into a wreath of beautiful little luminous flowers, like forget-me-nots. To make this experiment, you will be obliged to have a tube with a larger opening than that at F.
This instrument will afford you many an hour of instruction and amusement. We have only space to show you a few experiments. Others will suggest themselves whenever you use it.
Experiment 114.—Sing into the funnel the sound of oo as in pool. After a few trials you will get a pure simple sound, and the flame will appear as in Fig. 52. Some voices get this figure more readily by singing E.
Experiment 115.—Twirling the mirror with the same velocity, gradually lower the pitch of the oo sound till your voice falls to its lower octave, when the flame will appear as in Fig. 53, with half the number of teeth in Fig. 52, because the lower octave of a sound is given by half the number of vibrations.
Experiment 116.—Sing the vowel-sound o on the note and you will see Fig. 54 in the mirror. This evidently is not the figure that would have been made by a simple vibration. It shows that this o sound is compound, and formed of two simple sounds, one the octave of the other. The larger teeth are made by every alternate vibration of the higher simple sound acting with a vibration of the lower, and thus making the flame jump higher by their combined action on the membrane.
Experiment 117.—Fig. 55 appears on the mirror when we sing the English vowel a on the note f.
Experiment 118.—Fig. 56 appears on the mirror when we sing the English vowel a on the note c.
Examine attentively Fig. 55. This shows that the English vowel a sung on f is made up of two combined simple vibrations. One of these alone would make the long tongues of flame, but with this simple vibration exists another of three times its frequency; that is, the vibration of greater frequency is the third harmonic of the slower. As the slower vibration, making the long tongues of flame, is f, the higher
Figs. 52, 53, 54, 55, 56.
must be c" of the second octave above f. Each third vibration of this higher harmonic coincides with each vibration of f; hence each third tongue of flame is higher than the others.
Experiment 119.—In like manner the student must analyze Fig. 56 into its simple sonorous elements. Then he should, with the vibrating flame, examine the peculiarities of the various voices of his friends, and make neat and accurate drawings of the flames corresponding to them, so that he may analyze them at his leisure.
Experiment 120.—Blow your toy trumpet into the paper cone gently, and then strongly, and observe that the sound given by the trumpet is a complex one. Try if you cannot get a flame somewhat like that the trumpet gives by singing ah, through your nose, into the cone.
The student will soon find that different persons, in singing the same note, as nearly alike as they can, will produce flames of very different forms. This is because the voices differ in the number and relative intensities of the simple sounds which form them.