Similar remarks apply to sonorous waves. If in two systems of sonorous waves condensation coincides with condensation, and rarefaction with rarefaction, the sound produced by such coincidence is louder than that produced by either system taken singly. But if the condensations of the one system coincide with the rarefactions of the other, a destruction, total or partial, of both systems is the consequence. Thus, when two organ-pipes of the same pitch are placed near each other on the same wind-chest and thrown into vibration, they so influence each other that as the air enters the embouchure of the one it quits that of the other. At the moment, therefore, the one pipe produces a condensation the other produces a rarefaction. The sounds of two such pipes mutually destroy each other. When two musical sounds of nearly the same pitch are sounded together the flow of the sound is disturbed by _beats_. These beats are due to the alternate coincidence and interference of the two systems of sonorous waves. If the two sounds be of the same intensity, their coincidence produces a sound of four times the intensity of either; while their opposition produces absolute silence. The effect, then, of two such sounds, in combination, is a series of shocks, which we have called “beats,” separated from each other by a series of “pauses.” The rate at which the beats succeed each other is equal to the difference between the two rates of vibration. When a bell or disk sounds, the vibrations on opposite sides of the same nodal line partially neutralize each other; when a tuning-fork sounds, the vibrations of its two prongs in part neutralize each other. By cutting off a portion of the vibrations in these cases the sound may be intensified. When a luminous beam, reflected on to a screen from two tuning-forks producing beats, is acted upon by the vibrations of both, the intermittence of the sound is announced by the alternate lengthening and shortening of the band of light upon the screen. The law of the superposition of vibrations above enunciated is strictly true only when the amplitudes are exceedingly small. When the disturbance of the air by a sounding body is so violent that the law no longer holds good, secondary waves are formed, which correspond to the harmonic tones of the sounding body. When two tones are rendered so intense as to exceed the limits of the law of superposition, their secondary waves combine to produce _resultant tones_. Resultant tones are of two kinds; the one class corresponding to rates of vibration equal to the difference of the rates of the two primaries; the other class corresponding to rates of vibration equal to the sum of the two primaries. The former are called _difference-tones_, the latter _summation-tones_. CHAPTER IX