Tone, and Its Laws of Vibration
A tone is produced by a periodical motion of the sounding body—a noise by motions not periodical. We can see and feel the sounding vibrations of stationary bodies. The eye can perceive the vibrations of a string, and a person playing on a clarionet, oboe, or any similar instrument, feels the vibration of the reed of the mouthpiece. How the movements of the air, agitated by the vibrations of the stationary body, are felt by the ear as tone (Klang), Helmholtz illustrates by the motion of waves of water in the following way: Imagine a stone thrown into perfectly smooth water. Around the point of the surface struck by the stone there is instantly formed a little ring, which, moving outwards equally in all directions, spreads to an ever-enlarging circle. Corresponding to this ring, sound goes out in the air from an agitated point, and enlarges in all directions as far as the limits of the atmosphere permit. What goes on in the air is essentially the same that takes place on the surface of the water; the chief difference only is that sound spreads out in the spacious sea of air like a sphere, while the waves on the surface of the water can extend only like a circle. At the surface the mass of the water is free to rise upward, where it is compressed and forms billows, or crests. In the interior of the aerial ocean the air must be condensed, because it cannot rise. For, “in fact, the condensation of the sound-wave corresponds to the crest, while the rarefaction of the sound-wave corresponds to the sinus of the water-wave.” 7
The water-waves press continually onwards into the distance, but the particles of the water move to and fro periodically within narrow limits. One may easily see these two movements by observing a small piece of wood floating on water; the wood moves just as the particles of water in contact with it move. It is not carried along with the rings of the wave, but is tossed up and down, and at last remains in the same place where it was at the first. In a similar way, as the particles of water around the wood are moved by the ring only in passing, so the waves of sound spread onwards through new strata of air, while the particles of air, tossed to and fro by these waves as they pass, are never really moved by them from their first place. A drop falling upon the surface of the water creates in it only a single agitation; but when a regular series of drops falls upon it, every drop produces a ring on the water. Every ring passes over the surface just like its predecessor, and is followed by other rings in the same way. In this way there is produced on the water a regular series of rings ever expanding. As many drops as fall into the water in a second, so many waves will in a second strike a floating piece of wood, which will be just so many times tossed up and down, and thus have a periodical motion, the period of which corresponds with the interval at which the drops fall. In like manner a sounding body, periodically moved, produces a similar periodic movement, first of the air, and then of the drum in the ear; the duration of the vibrations constituting the movement must be the same in the ear as in the sounding body.