When the synchronism between fork and string is perfect, the vibrations of the string are steady and long-continued. A slight departure from synchronism, however, introduces unsteadiness, and the ventral segments, though they may show themselves for a time, quickly disappear.
Fig. 47.
In the experiments just executed the fork vibrated in the direction of the length of the string. Every forward stroke of the fork raised a protuberance, which ran to the fixed end of the string, and was there reflected; so that when the longitudinal impulses were properly timed they produced a transverse vibration. Let us consider this further. One end of this heavy cord is attached to a hook A, Fig. 47, fixed in the wall. Laying hold of the other end I stretch the cord horizontally, and then move my hand to and fro in the direction of the cord. It swings as a whole, and you may notice that always, when the cord is at the limit of its swing, the hand is in its most forward position. If it vibrate in a vertical plane, the hand, in order to time the impulses properly, must be at its forward limit at the moment the cord reaches the upper boundary, and also at the moment it reaches the lower boundary of its excursion. A little reflection will make it plain that, in order to accomplish this, the hand must execute a complete vibration while the cord executes a semi-vibration; in other words, the vibrations of the hand must be twice as rapid as those of the cord.
Precisely the same is true of our tuning-fork. When the fork vibrates in the direction of the string, the number of vibrations which it executes in a certain time is twice the number executed by the string itself. And if, while arranged thus, a fork and string vibrate with sufficient rapidity to produce musical notes, the note of the fork will be an octave above that of the string.
But if, instead of the hand being moved to and fro in the direction of this heavy cord, it is moved at right angles to that direction, then every upward movement of the hand coincides with an upward movement of the cord; every downward movement of the hand with a downward movement of the cord. In fact, the vibrations of hand and string, in this case, synchronize perfectly; and if the hand could emit a musical note, the cord would, emit a note of the same pitch. The same holds good when a vibrating fork is substituted for the vibrating hand.
Hence, if the string vibrate as a whole when the vibrations of the fork are along it, it will divide into two ventral segments when the vibrations are across it; or, more generally expressed, preserving the tension constant, whatever be the number of ventral segments produced by the fork when its vibrations are in the direction of the string, twice that number will be produced when the vibrations are transverse to the string. The string A B, for example, Figs. 48 and 49, passing over a pulley B, is stretched by a definite weight (not shown in the figure). When the tuning-fork vibrates along it, as in Fig. 48, the string divides into two equal ventral segments. When the fork is turned so that it shall vibrate at right angles to the string, the number of ventral segments is four, Fig. 49, or double the former number. Attaching two strings of the same length to the same fork, the one parallel and the other perpendicular to the direction of vibration, and stretching both with equal weights, when the fork is caused to vibrate, one of them divides itself into twice the number of ventral segments exhibited by the other.
Fig. 48.