Fig. 329.—Interference of sound waves.
Fig. 330.—At 2 is a condensation; at 1 and 3 are rarefactions.
Fig. 331.—The condensations and rarefactions meet along the dotted lines producing silence.
Fig. 332.—Diagram illustrating the formations of beats.
341. Beats.—If two tuning forks of slightly different pitch are set vibrating and placed over resonating air columns or with the stem of each fork upon a sounding board, so that the sounds may be intensified, a peculiar pulsation of the sound may be noticed. This phenomenon is known as beats. Its production may be easily understood by considering a diagram (Fig. 332). Let the curve A represent the sound wave sent out by one tuning fork and B, that sent out by the other. C represents the effect produced by the combination of these waves. At R the two sound waves meet in the same phase and reinforce each other. This results in a louder sound than either produces alone. Now since the sounds are of slightly different pitch, one fork sends out a few more vibrations per second than the other. The waves from the first fork are therefore a little shorter than those from the other. Consequently, although the two waves are at one time in the same phase, they must soon be in opposite phases as at I. Here interference occurs, and silence results. Immediately the waves reinforce, producing a louder sound and so on alternately. The resulting rise and fall of the sound are known as beats. The number of beats per second must, of course, be the same as the difference between the numbers of vibrations per second of the two sounds. One effect of beats is discord. This is especially noticeable when the number of beats per second is between 30 and 120. Strike the two lowest notes on a piano at the same time. The beats are very noticeable.
Fig. 333.—Turkish cymbals.
Fig. 334.—The cornet.
342. Three Classes of Musical Instruments.—There are three classes or groups of musical instruments, if we consider the vibrating body that produces the sound in each: (A) Those in which the sound is produced by a vibrating plate or membrane, as the drum, cymbals (Fig. 333), etc.; (B) those with vibrating air columns, as the flute, pipe organ, and cornet (Fig. 334), and (C) with vibrating wires or strings, as the piano, violin, and guitar. It is worth while to consider some of these carefully. We will begin with a consideration of vibrating wires and strings, these often producing tones of rich quality.
Let us consider the strings of a piano. (If possible, look at the strings in some instrument.) The range of the piano is 7-1/3 octaves. Its lowest note, A4, has about 27 vibrations per second. Its highest, C4, about 4176. This great range in vibration rate is secured by varying the length, the tension, and the diameter of the strings.