Letters of a Radio-Engineer to His Son

by John Mills

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 162complex 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 that 163there 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 164of 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.