So likewise the length of a solid rod free at both ends, and sounding its fundamental note, is half that of the sonorous wave in the substance of the solid. Hence we have only to determine the rate of vibration of such a rod, and multiply it by twice the length of the rod, to obtain the velocity of sound in the substance of the rod. You can hardly fail to be impressed by the power which physical science has given us over these problems; nor will you refuse your admiration to that famous old investigator, Chladni, who taught us how to master them experimentally.
REEDS AND REED-PIPES
The construction of the siren and our experiments with that instrument are, no doubt, fresh in your recollection. Its musical sounds are produced by the cutting up into puffs of a series of air-currents. The same purpose is effected by a vibrating reed, as employed in the accordion, the concertina, and the harmonica. In these instruments it is not the vibrations of the reed itself which, imparted to the air, and transmitted through it to our organs of hearing, produce the music; the function of the reed is constructive, not generative; it molds into a series of discontinuous puffs that which without it would be a continuous current of air.
Fig. 104.
Reeds, if associated with organ-pipes, sometimes command, and are sometimes commanded by, the vibrations of the column of air. When they are stiff they rule the column; when they are flexible the column rules them. In the former case, to derive any advantage from the air-column, its length ought to be so regulated that either its fundamental tone or one of its overtones shall correspond to the rate of vibration of the reed. The metal reed commonly employed in organ-pipes is shown in Fig. 104, A and b, both in perspective and in section. It consists of a long and flexible strip of metal, V V, placed in a rectangular orifice, through which the current of air enters the pipe. The manner in which the reed and pipe are associated is shown in Fig. 105. The front, b c, of the space containing the flexible tongue is of glass, so that you may see the tongue within it. A conical pipe, A B, surmounts the reed.[47] The wire w i, shown pressing
Fig. 105. against the reed, is employed to lengthen or shorten it, and thus to vary within certain limits its rate of vibration. At one time in the practice of music the reed closed the aperture by simply falling against its sides; every stroke of the reed produced a tap, and these linked themselves together to an unpleasant, screaming sound, which materially injured that of the associated organ-pipe. This was mitigated, but not removed, by permitting the reed to strike against soft leather; but the reed now employed is the free reed, which vibrates to and fro between the sides of the aperture, almost, but not quite, filling it. In this way the unpleasantness referred to is avoided. When reed and pipe synchronize perfectly, the sound is most pure and forcible; a certain latitude, however, is possible on both sides of perfect synchronism. But if the discordance be pushed too far, the pipe ceases to be of any use. We then obtain the sound due to the vibrations of the reed alone.
Flexible wooden reeds, which can accommodate themselves to the requirements of the pipes above them, are also employed in organ-pipes. Perhaps the simplest illustration of the action of the reed commanded by its aërial column is furnished by a common wheaten straw. At about an inch from a knot, at r, I bury my penknife in this straw, s r′, Fig. 106, to a depth of about one-fourth of the straw’s diameter, and, turning the blade flat, pass it upward toward the knot, thus raising a strip of the straw nearly an inch in length. This strip, r r′, is to be our reed, and the straw itself is to be our pipe. It is now eight inches long. When blown into, it emits this decidedly musical sound. When cut so as to make its length six inches, the pitch is higher; with a length of four inches, the pitch is higher still; and with a length of two inches, the sound is very shrill indeed. In these experiments the reed was compelled to accommodate itself throughout to the requirements of the vibrating column of air.
