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PROPERTIES OF MUSICAL SOUNDS
416. Vibrating reed instruments. In reed instruments the vibrating air jet is replaced by a vibrating reed, or tongue, which opens and closes, at absolutely regular intervals, an opening against which the performer is directing a current of air. In the clarinet, the oboe, the bassoon, etc. the reed is placed at the upper end of the tube (see 1, Fig. 369), and the theory of its opening and closing the orifice so as to admit successive puffs of air to the pipe is identical with the theory of the fluctuation of the air jet into and out of the organ pipe. For in these instruments the reed has little rigidity and its vibrations are controlled largely by the reflected pulses but partly by the reed and by the lips of the performer.
In other reed instruments, like the mouth organ, the common reed organ, or the accordion, it is the elasticity of the reed alone (see z, Fig. 370) which controls the emission of pulses. In such instruments there is no necessity for air chambers. The arrows of Fig. 370 indicate the direction of the air current which is interrupted as the reed vibrates between the positions z1 and 2
FIG. 371. The reed-organ pipe
In still other reed instruments, like the reed pipes used in large organs (Fig. 371), the period of the pulses is controlled partly by the elasticity of the reed and partly by the return of the reflected waves; in other words, the natural period of the reed is more or less coerced by the period of the reflected pulses. Within certain limits, therefore, such instruments may be tuned by changing the length of the vibrating reed without changing the length of the pipe. This is done by pushing the wire r up or down.
FIG. 372. The cornet
417. Vibrating lip instruments. In instruments of the bugle and cornet type the vibrating reed is replaced by the vibrating lips of the musician, the period of their vibration being controlled, precisely as in the organ pipe or the clarinet, by the period of the returning pulses. In the bugle the pipe length is fixed,
and because of the narrowness of the tube all bugle calls are played with overtones. In the cornet (Fig. 372) and in most forms of horns, valves a, b, c, worked by the fingers, vary the length of the pipe, and hence such instruments can produce as many series of fundamentals and overtones as there are possible tube lengths. In the trombone the variation of pitch is accomplished by blowing overtones and by changing the length of the tube by a sliding U-shaped portion.
418. The phonograph. In the original form of the phonograph the sound waves, collected by the cone, are carried to a thin metallic disk C (Fig. 373), exactly like a telephone diaphragm, which takes up very nearly the vibration form of the wave which strikes it. This vibration form is permanently impressed on the wax-coated cylinder M by means of a stylus D which is attached to the back of the disk. When the stylus is run a second time over the groove which it first made in the wax, it receives again and imparts to the disk the vibration form which first fell upon it. This is the principle of the
FIG. 374. Mechanism for forming gramophone records
The diamond point
FIG. 375. The Edison diamond reproducer
dictaphone and the ediphone, used to replace stenographers in business offices. The typist writes the letter by listening to the reproduction of the dictation.
In the most familiar of the modern forms of the phonograph (gramophone, etc.) the needle point D, instead of digging a groove in wax, vibrates back and forth (see Fig. 374) over a greased zinc disk. This wavy trace in the disk is etched out with chromic acid. Then a copper mold is made by the electrotyping process, and as many as a thousand facsimiles of the original wavy line are impressed on hard-rubber disks by heat and pressure. When the needle is again run over the disk, it follows along the wavy groove and transmits to the diaphragm C vibrations exactly like those which originally fell upon it. Spoken words and vocal and orchestral music are reproduced in pitch, loudness, and quality with wonderful exactness. This instrument is one of the many inventions of Thomas Edison (see opposite p. 316). The diamond-tip reproducer used with the hill-and-dale Edison disks is shown in Fig. 375.
QUESTIONS AND PROBLEMS
1. What proves that a musical note is transmitted as a wave motion? 2. What evidence have you that sound waves are longitudinal vibrations?
3. Why is the pitch of a sound emitted by a phonograph raised by increasing the speed of rotation of the disk?
4. What will be the relative lengths of a series of organ pipes which produce the eight notes of a diatonic scale?
5. Will the pitch of a pipe organ be the same in summer as on a cold day in winter? What could cause a difference?
6. Explain how an instrument like the bugle, which has an air column of unchanging length, may be made to produce several notes of different pitch, such as C, G, C', E', G'. (C is not often used.)
7. Why is the quality of an open organ pipe different from that of a closed organ pipe?
8. The velocity of sound in hydrogen is about four times as great as it is in air. If a C pipe is blown with hydrogen, what will be the pitch of the note emitted?
9. What effect will be produced on a phonograph record made with the instrument of Fig. 374 if the loudness of a note is increased? if the pitch is lowered an octave?
NATURE AND PROPAGATION OF LIGHT
TRANSMISSION OF LIGHT
419. Speed of light. Before the year 1675 light was thought to pass instantaneously from the source to the observer. In that year, however, Olaus Römer, a young Danish astronomer, made the following observations. He had observed accurately the instant at which one of Jupiter's satellites M (Fig. 376) passed into Jupiter's shadow when the earth was at E, and predicted, from the known mean time between such eclipses, the exact instant at which a given eclipse should occur six months later when the earth was at E'. It actually took place 16 minutes 36
FIG. 376. Illustrating Römer's determination of the velocity of light
seconds (996 seconds) later. He concluded that the 996 seconds' delay represented the time required for light to travel across the earth's orbit, a distance known to be about 180,000,000 miles. The most precise of modern determinations of the speed of light are made by laboratory methods. The generally accepted value, that of Michelson, of The University of Chicago, is 299,860 kilometers per second. It is sufficiently correct to remember it as 300,000 kilometers, or 186,000 miles.
Though this speed would carry light around the earth 7 times in a second, yet it is so small in comparison with interstellar distances that the light which is now reaching the earth from the nearest fixed star, Alpha Centauri, started 4.4 years ago. If an observer on the pole star had a telescope powerful enough to enable him to see events on the earth, he would not have seen the battle of Gettysburg (which occurred in July, 1863) until January, 1918.
Both Foucault in France and Michelson in America have measured directly the velocity of light in water and have found it to be only three fourths as great as in air. It will be shown later that in all transparent liquids and solids it is less than it is in air.
420. Reflection of light.
Let a beam of sunlight be admitted to a darkened room through a narrow slit. The straight path of the beam will be rendered visible by the brightly illumined dust particles suspended in the air. Let the beam fall on the surface of a mirror. Its direction will be seen to be sharply changed, as shown in Fig. 377. Let the mirror be held so that it is perendicular to the beam. The beam will be seen to be reflected directly back on itself. Let the mirror be turned through an angle of 45°. The reflected beam will move through 90°.
The experiment shows roughly, therefore, that the angle IOP, between the incident beam and the normal to the mirror, is equal to the angle POR, between the reflected beam and the normal to the mirror. The first angle, IOP, is called the angle of incidence, and the second, POR, the angle of reflection. The angle of reflection is equal to the angle of incidence.
* An exact laboratory experiment on the law of reflection should either precede or follow this discussion. See, for example, Experiment 42 of the authors' Manual.