Fig. 341.—(R) Cross-section of an organ pipe showing action of tongue at C. (a) The fundamental tone in a closed pipe has a wave length four times the length of the pipe; (b) and (c) how the first and second overtones are formed in a closed pipe; (d) the fundamental tone of an open pipe has a wave length equal to twice the length of the pipe; (e) and (f) first and second overtones of open pipe.
If an open organ pipe be sounded by blowing gently through it, a tone of definite pitch is heard. Now if one end is closed, on being sounded again the pitch is found to be an octave lower. Therefore, the pitch of a closed pipe is an octave lower than that of an open one of the same length.
350. Nodes in Organ Pipes.—Fig. 341, R represents a cross-section of a wooden organ pipe. Air is blown through A, and strikes against a thin tongue of wood C. This starts the jet of air vibrating thus setting the column of air in vibration so that the sound is kept up as long as air is blown through A. To understand the mode of vibration of the air column a study of the curve that represents wave motion (Fig. 342) is helpful Let AB represent such a curve, in this 2, 4 and 6 represent nodes or points of least vibration, while 1, 3 and 5 are antinodes or places of greatest motion. A full wave length extends from 1-5, or 2-6. Now in the open organ pipe (Fig. 341d), the end of the air column d is a place of great vibration or is an antinode. At the other end also occurs another place of great vibration or an antinode; between these two antinodes must be a place of least vibration or a node. The open air column therefore extends from antinode to antinode (or from 1-3) or is one-half a wave length. The closed air column (Fig. 341a) extends from a place of great vibration at a to a place of no vibration at the closed end. The distance from an antinode to a node is that from 1-2 on the curve and is one-fourth a wave length.
Fig. 342.—Graphic representation of sound waves.
Fig. 343.—A clarinet.
When a pipe is blown strongly it yields overtones. The bugle is a musical instrument in which notes of different pitch are produced by differences in blowing. (See Fig. 341.) (d), (e), (f). In playing the cornet different pitches are produced by differences in blowing, and by valves which change the length of the vibrating air column. (See Fig. 334.) The clarinet has a mouthpiece containing a reed similar to that made by cutting a tongue on a straw or quill. The length of the vibrating air column in the clarinet is changed by opening holes in the sides of the tube. (See Fig. 343.)
351. How we Hear.—Our hearing apparatus is arranged in three parts. (See Fig. 344.) The external ear leads to the tympanum. The middle ear contains three bones that convey the vibrations of the tympanum to the internal ear. The latter is filled with a liquid which conveys the vibrations to a part having a coiled shell-like structure called the Cochlea. Stretched across within the cochlea are some 3000 fibers or strings. It is believed that each is sensitive to a particular vibration rate and that each is also attached to a nerve fiber. The sound waves of the air transmitted by the tympanum, the ear bones and the liquid of the internal ear start sympathetic vibrations in the strings of the cochlea which affect the auditory nerve and we hear. The highest tones perceptible by the human ear are produced by from 24,000 to 40,000 vibrations per second. The average person cannot hear sounds produced by more than about 28,000 vibrations. The usual range of hearing is about 11 octaves. The tones produced by higher vibrations than about 4100 per second are shrill and displeasing. In music the range is 7-1/3 octaves, the lowest tone being produced by 27.5 vibrations, the highest by about 4100 per second.
