through the ends of the prongs. As indicated above, these positions may be easily found by rotating a vibrating fork over a resonant air column, or near the ear. [Illustration: FIG. 329.--Interference of sound waves.] [Illustration: FIG. 330.--At 2 is a condensation; at 1 and 3 are rarefactions.] [Illustration: FIG. 331.--The condensations and rarefactions meet along the dotted lines producing silence.] [Illustration: 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. [Illustration: FIG. 333.--Turkish cymbals.] [Illustration: 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.