When the grid is positive, that is for half a cycle of the alternating grid-voltage, the stream is larger than it would be if the plate current depended only on the B-battery. For the other half of a cycle it is less. The question I am raising is this: Do more electrons move around the plate circuit if there is a signal coming in than when there is no incoming signal? To answer this we must look at the audion characteristic of our particular tube and this characteristic must have been taken with the same B-battery as we use when we try to receive the signals.
There are just three possible answers to this question. The first answer is: “No, there is a smaller number of electrons passing through the plate circuit each second if the grid is being affected by an incoming signal.” The second is: “The signal130doesn’t make any difference in the total number of electrons which move each second from filament to plate.” And the third answer is: “Yes, there is a greater total number each second.”
Any one of the three answers may be right. It all depends on the characteristic of the tube as we are operating it, and that depends not only upon the type and design of tube but also upon what voltages we are using in our batteries. Suppose the variations in the voltage of the grid are as represented in Fig. 55, and that the characteristic of the tube is as shown in the same figure. Then obviously the first answer is correct. You can see for yourself that when the grid becomes positive the current in the plate circuit can’t increase much anyway. For the other half of the cycle, that is, while the grid is negative, the current in the plate is very much decreased. The decrease in one half-cycle is larger than the increase during the other half-cycle, so that on the average the current is less when the131signal is coming in. The dotted line shows the average current.
Suppose that we take the same tube and use a B-battery of lower voltage. The characteristic will have the same shape but there will not be as much current unless the grid helps, so that the characteristic will be like that of Fig. 56. This characteristic crosses the axis of zero volts at a smaller number of mil-amperes than does the other because the B-batteries can’t pull as hard as they did in the other case.
You can see the result. When the grid becomes positive it helps and increases the plate current. When it becomes negative it opposes and decreases the plate current. But the increase just balances the decrease, so that on the average the current is unchanged, as shown by the dotted line.
On the other hand, if we use a still smaller voltage of B-battery we get a characteristic which shows a still smaller current when the grid is at zero potential.132For this case, as shown in Fig. 57, the plate current is larger on the average when there is an incoming signal.
If we want to know whether or not there is any incoming signal we will not use the tube in the second condition, that of Fig. 56, because it won’t tell us anything. On the other hand why use the tube under the first conditions where we need a large plate battery? If we can get the same result, that is an indication when the other station is signalling, by using a small battery let’s do it that way for batteries cost money. For that reason we shall confine ourselves to the study of what takes place under the conditions of Fig. 57.
We now know that when a signal is being sent by the distant station the current in the plate circuit of our audion at the receiving station is greater, on the average. We are ready to see what effect this has on the telephone receiver. And to do this requires a little study of how the telephone receiver works and why.
I shall not stop now to tell you much about the telephone receiver for it deserves a whole letter all to itself. You know that a magnet attracts iron. Suppose you wind a coil of insulated wire around a bar magnet or put the magnet inside such a coil as in Fig. 58. Send a stream of electrons through the turns of the coil–a steady stream such as comes from the battery shown in133the figure. The strength of the magnet is altered. For one direction of the electron stream through the coil the magnet is stronger. For the opposite direction of current the magnet will be weaker.
Fig. 59 shows a simple design of telephone receiver. It is formed by a bar magnet, a coil about it through which a current can flow, and a thin disc of iron. The iron disc, or diaphragm, is held at its edges so that it cannot move as a whole toward the magnet. The center can move, however, and so the diaphragm is bowed out in the form shown in the smaller sketch.
Now connect a battery to the receiver winding and allow a steady stream of electrons to flow. The magnet will be either strengthened or weakened. Suppose the stream of electrons is in the direction to make it stronger–I’ll give you the rule later. Then the diaphragm is bowed out still more. If we open the battery circuit and so stop the stream of electrons the diaphragm will fly back to its original position, for it is elastic. The effect is very much that of pushing in the bottom of a tin pan and letting it fly back when you remove your hand.
Next reverse the battery. The magnet does not pull as hard as it would if there were no current. The diaphragm is therefore not bowed out so much.
Suppose that instead of reversing the current by reversing the battery we arrange to send an alternating134current through the coil. That will have the same effect. For one direction of current flow, the diaphragm is attracted still more by the magnet but for the other direction it is not attracted as much. The result is that the center of the diaphragm moves back and forth during one complete cycle of the alternating current in the coil.
The diaphragm vibrates back and forth in tune with the alternating current in the receiver winding. As it moves away from the magnet it pushes ahead of it the neighboring molecules of air. These molecules then crowd and push the molecules of air which are just a little further away from the diaphragm. These in turn push against those beyond them and so a push or shove is sent out by the diaphragm from molecule to molecule until perhaps it reaches your ear. When the molecules of air next your ear receive the push they in turn push against your eardrum.
In the meantime what has happened? The current in the telephone receiver has reversed its direction. The diaphragm is now pulled toward the magnet and the adjacent molecules of air have even more room than they had before. So they stop crowding each other and follow the diaphragm in the other direction. The molecules of air just beyond these, on the way toward your ear, need crowd no longer and they also move back. Of course, they go even farther than their old positions for there is now more room on the other side. That same thing happens all along the line until the air molecules next your ear start back and give your eardrum a chance135to expand outward. As they move away they make a little vacuum there and the eardrum puffs out.
That goes on over and over again just as often as the alternating current passes through one cycle of values. And you, unless you are thinking particularly of the scientific explanations, say that you “hear a musical note.” As a matter of fact if we increase the frequency of the alternating current you will say that the “pitch” of the note has been increased or that you hear a note higher in the musical scale.
If we started with a very low-frequency alternating current, say one of fifteen or twenty cycles per second, you wouldn’t say you heard a note at all. You would hear a sort of a rumble. If we should gradually increase the frequency of the alternating current you would find that about sixty or perhaps a hundred cycles a second would give you the impression of a musical note. As the frequency is made still larger you have merely the impression of a higher-pitched note until we get up into the thousands of cycles a second. Then, perhaps about twenty-thousand cycles a second, you find you hear only a little sound like wind or like steam escaping slowly from a jet or through a leak. A few thousand cycles more each second and you don’t hear anything at all.
You know that for radio-transmitting stations we use audion oscillators which are producing alternating currents with frequencies of several hundred-thousand cycles per second. It certainly wouldn’t do any good to connect a telephone receiver in the136antenna circuit at the receiving station as in Fig. 60. We couldn’t hear so high pitched a note.
Even if we could, there are several reasons why the telephone receiver wouldn’t work at such high frequencies. The first is that the diaphragm can’t be moved so fast. It has some inertia, you know, that is, some unwillingness to get started. If you try to start it in one direction and, before you really get it going, change your mind and try to make it go in the other direction, it simply isn’t going to go at all. So even if there is an alternating current in the coil around the magnet there will not be any corresponding vibration of the diaphragm if the frequency is very high, certainly not if it is above about 20,000 cycles a second.
The other reason is that there will only be a very feeble current in the coil anyway, no matter what you do, if the frequency is high. You remember that the electrons in a coil are sort of banded together and each has an effect on all the others which can move in parallel paths. The result is that they have a great unwillingness to get started and an equal unwillingness to stop. Their unwillingness is much more than if the wire was long and straight. It is also made very much greater by the presence of the iron core. An alternating e. m. f. of high frequency hardly gets the electrons started at all before it’s137time to get them going in the opposite direction. There is very little movement to the electrons and hence only a very small current in the coil if the frequency is high.
If you want a rule for it you can remember that the higher the frequency of an alternating e. m. f. the smaller the electron stream which it can set oscillating in a given coil. Of course, we might make the e. m. f. stronger, that is pull and shove the electrons harder, but unless the coil has a very small inductance or unless the frequency is very low we should have to use an e. m. f. of enormous strength to get any appreciable current.
Condensers are just the other way in their action. If there is a condenser in a circuit, where an alternating e. m. f. is active, there is lots of trouble if the frequency is low. If, however, the frequency is high the same-sized current can be maintained by a smaller e. m. f. than if the frequency is low. You see, when the frequency is high the electrons hardly get into the waiting-room of the condenser before it is time for them to turn around and go toward the other room. Unless there is a large current, there are not enough electrons crowded together in the waiting-room to push back very hard on the next one to be sent along by the e. m. f. Because the electrons do not push back very hard a small e. m. f. can drive them back and forth.
Ordinarily we say that a condenser impedes an alternating current less and less the higher is the frequency of the current. And as to inductances, we say that an inductance impedes an alternating current138more and more the higher is the frequency.
Now we are ready to study the receiving circuit of Fig. 54. I showed you in Fig. 57 how the current through, the tube will vary as time goes on. It increases and decreases with the frequency of the current in the antenna of the distant transmitting station. We have a picture, or graph, as we say, of how this plate current varies. It will be necessary to study that carefully and to resolve it into its components, that is to separate it into parts, which, added together again will give the whole. To show you what I mean I am going to treat first a very simple case involving money.
Suppose a boy was started by his father with 50 cents of spending money. He spends that and runs 50 cents in debt. The next day his father gives him a dollar. Half of this he has to spend to pay up his yesterday’s indebtedness. This he does at once and that leaves him 50 cents ahead. But again he buys something for a dollar and so runs 50 cents in debt. Day after day this cycle is repeated. We can show what happens by the curve of Fig. 61a.
On the other hand, suppose he already had 60 cents which, he was saving for some special purpose. This he doesn’t touch, preferring to run into debt each day and to pay up the next, as shown in Fig. 61a. Then we would represent the story of this 60 cents by the graph of Fig. 61b.
139Now suppose that instead of going in debt each day he uses part of this 60 cents. Each day after the first his father gives him a dollar, just as before. He starts then with 60 cents as shown in Fig. 61c, increases in wealth to $1.10, then spends $1.00, bringing his funds down to 10 cents. Then he receives $1.00 from his father and the process is repeated cyclically.
If you saw the graph of Fig. 61c you would be able to say that, whatever he actually did, the effect was the same as if he had two pockets, in one of which he kept 60 cents all the time as shown in Fig. 61b. In his other pocket he either had money or he was in debt as shown in Fig. 61a. If you did that you would be resolving the money changes of Fig. 61c into the two components of Figs. 61a and b.
That is what I want you to do with the curve of Fig. 57 which I am reproducing here, redrawn as Fig. 62a. You see it is really the result of adding together the two curves of Figs. 62b and c, which are shown on the following page.
We can think, therefore, of the current in the plate circuit as if it were two currents added together, that is, two electron streams passing through the same140wire. One stream is steady and the other alternates.
Now look again at the diagram of our receiving set which I am reproducing as Fig. 63. When the signal is incoming there flow in the plate circuit two streams of electrons, one steady and of a value in mil-amperes corresponding to that of the graph in Fig. 62b, and the other alternating as shown in Fig. 62c.
The steady stream of electrons will have no more difficulty in getting through the coiled wire of the receiver than it would through the same amount of straight wire. On the other hand it cannot pass the gap of the condenser.
The alternating-current component can’t get along in the coil because its frequency is so high that the coil impedes the motion of the electrons so much as practically to stop them. On the other hand these electrons can easily run into the waiting-room offered by the condenser and then run out again as soon as it is time.
When the current in the plate circuit is large all the electrons which aren’t needed for the steady stream through the telephone receiver run into one plate of the condenser. Of course, at that same instant an equal number leave the other plate and start off toward the B-battery and the filament. An instant later, when the current in the plate circuit is small, electrons start to come out of the141plate and to join the stream through the receiver so that this stream is kept steady.
This steady stream of electrons, which is passing through the receiver winding, is larger than it would be if there was no incoming radio signal. The result is a stronger pull on the diaphragm of the receiver. The moment the signal starts this diaphragm is pulled over toward the magnet and it stays pulled over as long as the signal lasts. When the signal ceases it flies back. We would hear then a click when the signal started and another when it stopped.
If we wanted to distinguish dots from dashes this wouldn’t be at all satisfactory. So in the next letter I’ll show you what sort of changes we can make in the apparatus. To understand what effect these changes will have you need, however, to understand pretty well most of this letter.
Dear Lad:
Before we start on the important subject matter of this letter let us make a short review of the preceding two letters.
An oscillating audion at the transmitting station produces an effect on the plate current of the detector audion at the receiving station. There is impressed upon the grid of the detector an alternating e. m. f. which has the same frequency as the alternating current which is being produced at the sending station. While this e. m. f. is active, and of course it is active only while the sending key is held down, there is more current through the winding of the telephone receiver and its diaphragm is consequently pulled closer to its magnet.
What will happen if the e. m. f. which is active on the grid of the detector is made stronger or weaker? The pull on the receiver diaphragm will be stronger or weaker and the diaphragm will have to move accordingly. If the pull is weaker the elasticity of the iron will move the diaphragm away from the magnet, but if the pull is stronger the diaphragm will be moved toward the magnet.
Every time the diaphragm moves it affects the air in the immediate neighborhood of itself and that air143in turn affects the air farther away and so the ear of the listener. Therefore if there are changes in the intensity or strength of the incoming signal there are going to be corresponding motions of the receiver diaphragm. And something to listen, too, if these changes are frequent enough but not so frequent that the receiver diaphragm has difficulty in following them.
There are many ways of affecting the strength of the incoming signal. Suppose, for example, that we arrange to decrease the current in the antenna of the transmitting station. That will mean a weaker signal and a smaller increase in current through the winding of the telephone receiver at the other station. On the other hand if the signal strength is increased there is more current in this winding.
Suppose we connect a fine wire in the antenna circuit as in Fig. 64 and have a sliding contact as shown. Suppose that when we depress the switch in the oscillator circuit and so start the oscillations that the sliding contact is atoas shown. Corresponding to that strength of signal there is a certain value of current through the receiver winding at the other station. Now let us move the slider, first toaand then back toband so on, back and forth. You see what will happen. We alternately make the current in the antenna144larger and smaller than it originally was. When the slider is atbthere is more of the fine wire in series with the antenna, hence more resistance to the oscillations of the electrons, and hence a smaller oscillating stream of electrons. That means a weaker outgoing signal. When the slider is atathere is less resistance in the antenna circuit and a larger alternating current.
A picture of what happens would be like that of Fig. 65. The signal varies in intensity, therefore, becoming larger and smaller alternately. That means the voltage impressed on the grid of the detector is alternately larger and smaller. And hence the stream of electrons through the winding of the telephone receiver is alternately larger and smaller.145And that means that the diaphragm moves back and forth in just the time it takes to move the slider back and forth.
Instead of the slider we might use a little cup almost full of grains of carbon. The carbon grains lie between two flat discs of carbon. One of these discs is held fixed. The other is connected to the center of a thin diaphragm of steel and moves back and forth as this diaphragm is moved. The whole thing makes a telephone transmitter such as you have often talked to.
Wires connect to the carbon discs as shown in Fig. 66. A stream of electrons can flow through the wires and from grain to grain through the “carbon button,” as we call it. The electrons have less difficulty if the grains are compressed, that is the button then offers less resistance to the flow of current. If the diaphragm moves back, allowing the grains to have more room, the electron stream is smaller and we say the button is offering more resistance to the current.
You can see what happens. Suppose some one talks into the transmitter and makes its diaphragm go back and forth as shown in Fig. 67a. Then the current in the antenna varies, being greater or less, depending upon whether the button offers less or146more resistance. The corresponding variations in the antenna current are shown in Fig. 67b.
In the antenna at the receiving station there are corresponding variations in the strength of the signal and hence corresponding variations in the strength of the current through the telephone receiver. I shall show graphically what happens in Fig. 68. You see that the telephone receiver diaphragm does just the same motions as does the transmitter diaphragm. That means that the molecules of air near the receiver diaphragm are going through just the same kind of motions as are those near the transmitter diaphragm. When these air molecules affect your eardrum you hear just what you would have heard if you had been right there beside the transmitter.
That’s one way of making a radio-telephone. It is not a very efficient method but it has been used in the past. Before we look at any of the more recent methods we can draw some general ideas from this method and learn some words that are used almost always in speaking of radio-telephones.
In any system of radio-telephony you will always find that there is produced at the transmitting station a high-frequency alternating current and that this current flows in a tuned circuit one part of which is the condenser formed by the antenna and the ground (or something which acts like a ground). This high-frequency current, or radio-current, as we usually say, is varied in its strength. It is varied in conformity with the human voice. If the human147voice speaking into the transmitter is low pitched there are slow variations in the intensity of the radio current. If the voice is high pitched there are more rapid variations in the strength of the radio-frequency current. That is why we say the radio-current is “modulated” by the human voice.
The signal which radiates out from the transmitting antenna carries all the little variations in pitch and loudness of the human voice. When this signal reaches the distant antenna it establishes in that antenna circuit a current of high frequency which has just the same variations as did the current in the antenna at the sending station. The human voice isn’t there. It is not transmitted. It did its work at the sending station by modulating the radio-signal,148“modulating the carrier current,” as we sometimes say. But there is speech significance hidden in the variations in strength of the received signal.
If a telephone-receiver diaphragm can be made to vibrate in accordance with the variations in signal intensity then the air adjacent to that diaphragm will be set into vibration and these vibrations will be just like those which the human voice set up in the air molecules near the mouth of the speaker. All the different systems of receiving radio-telephone signals are merely different methods of getting a current which will affect the telephone receiver in conformity with the variations in signal strength. Getting such a current is called “detecting.” There are many different kinds of detectors but the vacuum tube is much to be preferred.
The cheapest detector, but not the most sensitive, is the crystal. If you understand how the audion works as a detector you will have no difficulty in understanding the crystal detector.
The crystal detector consists of some mineral crystal and a fine-wire point, usually platinum. Crystals are peculiar things. Like everything else they are made of molecules and these molecules of atoms. The atoms are made of electrons grouped around nuclei which, in turn, are formed by close groupings of protons and electrons. The great difference between crystals and substances which are not crystalline, that is, substances which don’t have a special natural shape, is this: In crystals the molecules and atoms are all arranged in some orderly manner.149In other substances, substances without special form, amorphous substances, as we call them, the molecules are just grouped together in a haphazard way.
For some crystals we know very closely indeed how their molecules or rather their individual atoms are arranged. Sometime you may wish to read how this was found out by the use of X-rays.[6]Take the crystal of common salt for example. That is well known. Each molecule of salt is formed by an atom of sodium and one of chlorine. In a crystal of salt the molecules are grouped together so that a sodium atom always has chlorine atoms on every side of it, and the other way around, of course.
Suppose you took a lot of wood dumb-bells and painted one of the balls of each dumb-bell black to stand for a sodium atom, leaving the other unpainted150to stand for a chlorine atom. Now try to pile them up so that above and below each black ball, to the right and left of it, and also in front and behind it, there shall be a white ball. The pile which you would probably get would look like that of Fig. 69. I have omitted the gripping part of each dumbell because I don’t believe it is there. In my picture each circle represents the nucleus of an atom. I haven’t attempted to show the planetary electrons. Other crystals have more complex arrangements for piling up their molecules.
Now suppose we put two different kinds of substances close together, that is, make contact between them. How their electrons will behave will depend entirely upon what the atoms are and how they are piled up. Some very curious effects can be obtained.
The one which interests us at present is that across the contact points of some combinations of substances it is easier to get a stream of electrons to flow one way than the other. The contact doesn’t have the same resistance in the two directions. Usually also the resistance depends upon what voltage we are applying to force the electron stream across the point of contact.
The one way to find out is to take the voltage-current characteristic of the combination. To do so we use the same general method as we did for the audion.151And when we get through we plot another curve and call it, for example, a “platinum-galena characteristic.” Fig. 70 shows the set-up for making the measurements. There is a group of batteries arranged so that we can vary the e. m. f. applied across the contact point of the crystal and platinum. A voltmeter shows the value of this e. m. f. and an ammeter tells the strength of the electron stream. Each time we move the slider we get a new pair of values for volts and amperes. As a matter of fact we don’t get amperes or even mil-amperes; we get millionths of an ampere or “microamperes,” as we say. We can plot the pairs of values which we measure and make a curve like that of Fig. 71.
When the voltage across the contact is reversed, of course, the current reverses. Part of the curve looks something like the lower part of an audion characteristic.
Now connect this crystal in a receiving circuit as in Fig. 72. We use an antenna just as we did for the audion and we tune the antenna circuit to the frequency of the incoming signal. The receiving circuit is coupled to the antenna circuit and is tuned to the same frequency. Whatever voltage there may be across the condenser of this circuit is applied to the crystal detector. We haven’t put the telephone152receiver in the circuit yet. I want to wait until you have seen what the crystal does when an alternating voltage is applied to it.
We can draw a familiar form of sketch as in Fig. 73 to show how the current in the crystal varies. You see that there flows through the crystal a current very much like that of Fig. 62a. And you know that such a current is really equivalent to two electron streams, one steady and the other alternating. The crystal detector gives us much the same sort of a current as does the vacuum tube detector of Fig. 54. The current isn’t anywhere near as large, however, for it is microamperes instead of mil-amperes.
Our crystal detector produces the same results so far as giving us a steady component of current to send through a telephone receiver. So we can connect a receiver in series with the crystal as shown in Fig. 74. Because the receiver would offer a large impedance to the high-frequency current, that is, seriously impede and so reduce the high-frequency current, we connect a condenser around the receiver.
There is a simple crystal detector circuit. If the signal intensity varies then the current which passes through the receiver will vary. If these variations are caused by a human voice at the sending station the crystal will permit one to hear153from the telephone receiver what the speaker is saying. That is just what the audion detector does very many times better.
In the letter on how to experiment you’ll find details as to the construction of a crystal-detector set. Excellent instructions for an inexpensive set are contained in Bull. No. 120 of the Bureau of Standards. A copy can be obtained by sending ten cents to the Commissioner of Public Documents, Washington, D. C.
[6]Cf. “Within the Atom,” Chapter X.
Cf. “Within the Atom,” Chapter X.
Dear Sir:
The radio-telephone does not transmit the human voice. It reproduces near the ears of the listener similar motions of the air molecules and hence causes in the ears of the listener the same sensations of sound as if he were listening directly to the speaker. This reproduction takes place almost instantaneously so great is the speed with which the electrical effects travel outward from the sending antenna. If you wish to understand radio-telephony you must know something of the mechanism by which the voice is produced and something of the peculiar or characteristic properties of voice sounds.
The human voice is produced by a sort of organ pipe. Imagine a long pipe connected at one end to a pair of fire-bellows, and closed at the other end by two stretched sheets of rubber. Fig. 75 is a sketch of155what I mean. Corresponding to the bellows there is the human diaphragm, the muscular membrane separating the thorax and abdomen, which expands or contracts as one breathes. Corresponding to the pipe is the windpipe. Corresponding to the two stretched pieces of rubber are the vocal cords, L and R, shown in cross section in Fig. 77. They are part of the larynx and do not show in Fig. 76 (Pl. viii) which shows the wind pipe and an outside view of the larynx.
When the sides of the bellows are squeezed together the air molecules within are crowded closer together and the air is compressed. The greater the compression the greater, of course, is the pressure with which the enclosed air seeks to escape. That it can do only by lifting up, that is by blowing out, the two elastic strips which close the end of the pipe.
The air pressure, therefore, rises until it is sufficient to push aside the elastic membranes or vocal cords and thus to permit some of the air to escape. It doesn’t force the membranes far apart, just enough to let some air out. But the moment some air has escaped there isn’t so much inside and the pressure is reduced just as in the case of an automobile tire from which you let the air escape. What is the result? The membranes fly back again and156close the opening of the pipe. What got out, then, was just a little puff of air.
The bellows are working all the while, however, and so the space available for the remaining air soon again becomes so crowded with air molecules that the pressure is again sufficient to open the membranes. Another puff of air escapes.
This happens over and over again while one is speaking or singing. Hundreds of times a second the vocal cords vibrate back and forth. The frequency with which they do so determines the note or pitch of the speaker’s voice.
What determines the significance of the sounds which he utters? This is a most interesting question and one deserving of much more time than I propose to devote to it. To give you enough of an answer for your study of radio-telephony I am going to tell you first about vibrating strings for they are easier to picture than membranes like the vocal cords.
Suppose you have a stretched string, a piece of rubber band or a wire will do. You pluck it, that is pull it to one side. When you let go it flies back. Because it has inertia[7]it doesn’t stop when it gets to its old position but goes on through until it bows out almost as far on the other side.
Pl. VII.–Photographs of Vibrating Strings.
Pl. VII.–Photographs of Vibrating Strings.
157It took some work to pluck this string, not much perhaps; but all the work which you did in deforming it, goes to the string and becomes its energy, its ability to do work. This work it does in pushing the air molecules ahead of it as it vibrates. In this way it uses up its energy and so finally comes again to rest. Its vibrations “damp out,” as we say, that is die down. Each swing carries it a smaller distance away from its original position. We say that the “amplitude,” meaning the size, of its vibration decreases. The frequency does not. It takes just as long for a small-sized vibration as for the larger. Of course, for the vibration of large amplitude the string must move faster but it has to move farther so that the time required for a vibration is not changed.
First the string crowds against each other the air molecules which are in its way and so leads to crowding further away, just as fast as these molecules can pass along the shove they are receiving. That takes place at the rate of about 1100 feet a second. When the string swings back it pushes away the molecules which are behind it and so lets those that were being crowded follow it. You know that they will. Air molecules will always go where there is the least crowding. Following the shove, therefore, there is a chance for the molecules to move back and even to occupy more room than they had originally.
The news of this travels out from the string just as fast as did the news of the crowding. As fast as molecules are able they move back and so make more room for their neighbors who are farther away; and these in turn move back.
Do you want a picture of it? Imagine a great crowd of people and at the center some one with authority. The crowd is the molecules of air and the158one with authority is one of the molecules of the string which has energy. Whatever this molecule of the string says is repeated by each member of the crowd to his neighbor next farther away. First the string says: “Go back” and each molecule acts as soon as he gets the word. And then the string says: “Come on” and each molecule of air obeys as soon as the command reaches him. Over and over this happens, as many times a second as the string makes complete vibrations.
If we should make a picture of the various positions of one of these air molecules much as we pictured “Brownie” in Letter 9 it would appear as in Fig. 78a where the central line represents the ordinary position of the molecule.
That’s exactly the picture also of the successive positions of an electron in a circuit which is “carrying an alternating current.” First it moves in one direction along the wire and then back in the opposite direction. The electron next to it does the same thing almost immediately for it does not take anywhere near as long for such an effect to pass through a crowd of electrons. If we make the string vibrate twice as fast, that is, have twice the frequency, the story of an adjacent particle of air will be as in Fig. 78b. Unless we tighten the string, however, we can’t make it vibrate159as a whole and do it twice as fast. We can make it vibrate in two parts or even in more parts, as shown in Fig. 79 of Pl. VII. When it vibrates as a whole, its frequency is the lowest possible, the fundamental frequency as we say. When it vibrates in two parts each part of the string makes twice as many vibrations each second. So do the adjacent molecules of air and so does the eardrum of a listener.
The result is that the listener hears a note of twice the frequency that he did when the string was vibrating as a whole. He says he hears the “octave” of the note he heard first. If the string vibrates in three parts and gives a note of three times the frequency the listener hears a note two octaves above the “fundamental note” of which the string is capable.
It is entirely possible, however, for a string to vibrate simultaneously in a number of ways and so to give not only its fundamental note but several others at the same time. The photographs[8]of Fig. 80 of Pl. VII illustrate this possibility.
What happens then to the molecules of air which are adjacent to the vibrating string? They must perform quite complex vibrations for they are called upon to move back and forth just as if there were several strings all trying to push them with different frequencies of vibration. Look again at the pictures, of Fig. 80 and see that each might just as well be160the picture of several strings placed close together, each vibrating in a different way. Each of the strings has a different frequency of vibration and a different maximum amplitude, that is, greatest size of swing away from its straight position.
Suppose instead of a single string acting upon the adjacent molecules we had three strings. Suppose the first would make a nearby molecule move as in Fig. 81A, the second as in Fig. 81B, and the third as in Fig. 81C. It is quite evident that the molecule can satisfy all three if it will vibrate as in Fig. 81D.
161Now take it the other way around. Suppose we had a picture of the motion of a molecule and that it was not simple like those shown in Fig. 78 but was complex like that of Fig. 81D. We could say that this complex motion was made up of three parts, that is, had three component simple motions, each represented by one of the three other graphs of Fig. 81. That means we can resolve any complex vibratory motion into component motions which are simple.
It means more than that. It means that the vibrating string which makes the neighboring molecules of air behave as shown in Fig. 81D is really acting like three strings and is producing simultaneously three pure musical notes.
Now suppose we had two different strings, say a piano string in the piano and a violin string on its proper mounting. Suppose we played both instruments and some musician told us they were in tune. What would he mean? He would mean that both strings vibrated with the same fundamental frequency.
They differ, however, in the other notes which they produce at the same time that they produce their fundamental notes. That is, they differ in the frequencies and amplitudes of these other component vibrations or “overtones” which are going on at the same time as their fundamental vibrations. It is this difference which lets us tell at once which instrument is being played.
That brings us to the main idea about musical sounds and about human speech. The pitch of any162complex sound is the pitch of its fundamental or lowest sound; but the character of the complex sound depends upon all the overtones or “harmonics” which are being produced and upon their relative frequencies and amplitudes.
The organ pipe which ends in the larynx produces a very complex sound. I can’t show you how complex but I’ll show you in Fig. 82 the complicated motion of an air molecule which is vibrating as the result of being near an organ pipe. (Organ pipes differ–this is only one case.) You can see that163there are a large number of pure notes of various intensities, that is, strengths, which go to make up the sound which a listener to this organ pipe would hear. The note from the human pipe is much more complex.
When one speaks there are little puffs of air escaping from his larynx. The vocal cords vibrate as I explained. And the molecules of air near the larynx are set into very complex vibrations. These transmit their vibrations to other molecules until those in the mouth are reached. In the mouth, however, something very important happens.
Did you ever sing or howl down a rain barrel or into a long pipe or hallway and hear the sound? It sounds just about the same no matter who does it. The reason is that the long column of air in the pipe or barrel is set into vibration and vibrates according to its own ideas of how fast to do it. It has a “natural frequency” of its own. If in your voice there is a note of just that frequency it will respond beautifully. In fact it “resonates,” or sings back, when it hears this note.
The net result is that it emphasizes this note so much that you don’t hear any of the other component notes of your voice–all you hear is the rain barrel. We say it reinforces one of the component notes of your voice and makes it louder.
That same thing happens in the mouth cavity of a speaker. The size and shape of the column of air in the mouth can be varied by the tongue and lip positions and so there are many different possibilities164of resonance. Depending on lip and tongue, different frequencies of the complex sound which comes from the larynx are reinforced. You can see that for yourself from Fig. 83 which shows the tongue positions for three different vowel sounds. You can see also from Fig. 84, which shows the mouth positions for the different vowels, how the size and shape of the mouth cavity is changed to give different sounds. These figures are in Pl. VIII.
The pitch of the note need not change as every singer knows. You can try that also for yourself by singing the vowel sound of “ahh” and then changing the shape of your mouth so as to give the sound “ah–aw–ow–ou.” The pitch of the note will not change because the fundamental stays the same. The speech significance of the sound, however, changes completely because the mouth cavity resonates to different ones of the higher notes which come from the larynx along with the fundamental note.
Now you can see what is necessary for telephonic transmission. Each and every component note which enters into human speech must be transmitted and accurately reproduced by the receiver. More than that, all the proportions must be kept just the same as in the original spoken sound. We usually say that there must be reproduced in the air at the receiver exactly the same “wave form” as is present in the air at the transmitter. If that isn’t done the speech won’t be natural and one cannot recognize voices although he may understand pretty well. If165there is too much “distortion” of the wave form, that is if the relative intensities of the component notes of the voice are too much altered, then there may even be a loss of intelligibility so that the listener cannot understand what is being said.
What particular notes are in the human voice depends partly on the person who is speaking. You know that the fundamental of a bass voice is lower than that of a soprano. Besides the fundamental, however, there are a lot of higher notes always present. This is particularly true when the spoken sound is a consonant, like “s” or “f” or “v.” The particular notes, which are present and are important, depend upon what sound one is saying.
Usually, however, we find that if we can transmit and reproduce exactly all the notes which lie between a frequency of about 200 cycles a second and one of about 2000 cycles a second the reproduced speech will be quite natural and very intelligible. For singing and for transmitting instrumental music it is necessary to transmit and reproduce still higher notes.
What you will have to look out for, therefore, in a receiving set is that it does not cut out some of the high notes which are necessary to give the sound its naturalness. You will also have to make sure that your apparatus does not distort, that is, does not receive and reproduce some notes or “voice frequencies” more efficiently than it does some others which are equally necessary. For that reason when you buy a transformer or a telephone receiver it is166well to ask for a characteristic curve of the apparatus which will show how the action varies as the frequency of the current is varied. The action or response should, of course, be practically the same at all the frequencies within the necessary part of the voice range.