What Is Meant by the Length of Sound Waves?
The length of a sound wave embraces the distance from the point of greatest compression in one wave to the same point in the next. This depends upon the pitch for if a sounding body is making one hundred vibrations a second, by the time the one hundredth vibration is made, the wave from the first vibration will have travelled about eleven hundred feet from the starting point, and the remaining ninety-eight waves will lie between the first and the one hundredth. In consequence of this, the wave length for that particular sound will be about eleven feet. If the sounding body had made eleven hundred vibrations a second by the time the first wave had travelled eleven hundred feet, there would have been eleven hundred waves produced, and the wave length for that sound would be one foot. The wave lengths of sounds produced by the human voice usually lay between one and eight feet, though some singers have produced notes having wave lengths as great as eighteen feet, and others have reached notes so high that the wave length was only about nine inches.
When a tuning fork is struck, it produces a sound so faint that it can scarcely be heard unless the fork is held near the ear; but if the end of the fork is held on a box or table, the sound rings out loudly and seems to come from the table. The explanation of this is very simple. When only the fork vibrates, it produces very small sound waves, because its prongs are small and cut through the air. But when it is set on a box or table, its vibrations are communicated to the support, and the broader surface of the box or table sets a larger mass of air in vibration, and so amplifies the sound of the fork. When a surface is used in this way to reinforce the vibrations of a small body, and thus produce sound waves of greater volume, it is called a sounding board. Many musical instruments, like the violin and the piano, owe the intensity of their sounds to sounding boards, which reinforce the vibrations of their strings.
WHAT A SOUNDING BOARD DOES
Columns of air, like sounding boards, serve to reinforce sound waves. Unlike sounding boards, however, they do not respond equally well to a large number of different sounds. They respond to one sound only, or to several widely different ones. This may be shown as follows: Take a glass tube about sixteen inches long, and two inches in diameter, and after thrusting one end of it into a vessel of water, hold a vibrating tuning fork over the other end. By gradually lowering the tube into the water a point will be reached at which the sound becomes very loud, and as this point is passed the sound gradually dies away again. By raising the tube again the sound is again made loud when the tube reaches a certain point. This shows that to reinforce sound waves of a certain vibration frequency, the column of air in the tube must be of certain length.
Let us now see why the waves produced by the tuning fork are reinforced only by a column of air of a certain length. When the prongs of the fork make a vibration, a wave of air is produced which enters the tube, goes down to the water, is reflected, and comes back toward the fork. Now, if the reflected wave reaches the fork at the precise moment when it has completed one-half of its vibration and is about to begin upon the second half, it will strengthen the wave produced by the second half of the vibration; but if the reflected wave reaches the fork before or after the beginning of the second half of the vibration, it will not reinforce it. At the downward movement of the lower prong of the tuning fork, a wave of compression is sent down into the tube, and is reflected at the surface of the water. In order to reinforce the wave produced by the prong when it moves upward, the reflected wave must reach the fork just at the time that the prong reaches its normal position and before it starts upon the second half of its vibration.
Not only do columns of air tend to reinforce notes having a certain rate of vibration, but all elastic bodies have a certain rate at which they tend to vibrate, and when sounds having the same rate of vibration are produced near them, these bodies will vibrate in sympathy with them. If the sounds be kept up long enough, the sympathetic vibrations in objects near them sometimes become so great that they can easily be seen. Goblets and tumblers made of thin glass show this property very strikingly. When the proper notes are sounded the glasses take up the vibrations, and give a sound of the same pitch. If the note is loud, and is continued for some time, the vibrations of a glass sometimes become so great that the glass breaks. Large buildings, and bridges also, have rates at which they tend to vibrate, and this fact is the foundation for the old saying, that a man may fiddle a bridge down, if he fiddles long enough.