Letters of a Radio-Engineer to His Son Part 13

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 and close 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 s.p.a.ce 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.

[Ill.u.s.tration: Pl. VII.--Photographs of Vibrating Strings.]

It 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 pa.s.s 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 the one 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.

[Ill.u.s.tration: Fig 78]

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 pa.s.s 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 vibrate as 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 ill.u.s.trate 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 be the 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.

[Ill.u.s.tration: Fig 81]

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.

Now 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 any complex 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.

[Ill.u.s.tration: Fig 82]

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 that there 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 possibilities of 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. If there 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 ba.s.s 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 is well 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.

[Footnote 7: Cf. Chap. VI of "The Realities of Modern Science."]

[Footnote 8: My thanks are due to Professor D. C. Miller and to the Macmillan Company for permission to reproduce Figs. 79 to 83 inclusive from that interesting book, "The Science of Musical Sounds."]

LETTER 17

GRID BATTERIES AND GRID CONDENSERS FOR DETECTORS

DEAR SON:

You remember the audion characteristics which I used in Figs. 55, 56 and 57 of Letter 14 to show you how an incoming signal will affect the current in the plate circuit. Look again at these figures and you will see that these characteristics all had the same general shape but that they differed in their positions with reference to the "main streets" of "zero volts" on the grid and "zero mil-amperes" in the plate circuit.

Changing the voltage of the B-battery in the plate circuit changed the position of the characteristic. We might say that changing the B-battery shifted the curve with reference to the axis of zero volts on the grid.

[Ill.u.s.tration: Fig 56]

[Ill.u.s.tration: Fig 63]

In the case of the three characteristics which we are discussing the shift was made by changing the B-battery. Increasing B-voltage shifts characteristic to the left. It is possible, however, to produce such a shift by using a C-battery, that is, a battery in the grid circuit, which makes the grid permanently negative (or positive, depending upon how it is connected). This battery either helps or hinders the plate battery, and because of the strategic position of the grid right near the filament one volt applied to the grid produces as large an effect as would several volts in the plate battery. Usually, therefore, we arrange to shift the characteristic by using a C-battery.