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VII. § 76.] BEATS OF SIMPLE TONES. 157
therefore start on the next outward swing together, i.e. the vibrations will be momentarily in complete accordance. Thus, during the time requisite to enable B to perform one entire oscillation more than A, there occur the following changes. Complete accordance of vibrations, lasting only for a single swing of the more rapid pendulum, followed by partial accordance, in its turn gradually giving way to discordance, which culminates in complete opposition at the middle of the period, and then, during its latter half, gradually yields to returning accordance, which regains completeness just as the period closes.
It follows from this that, in the case of two simple tones differing slightly in pitch, we must hear a sound going through regularly recurring alternations of loudness in equal successive intervals of time, its greatest intensity exceeding, and its least intensity falling short of, that of the louder of the two tones. Each recurrence of the maximum intensity is called a beat, and it is clear that exactly one such beat will be heard in each interval of time during which the acuter of the two simple tones performs one more vibration than the graver tone. Accordingly, the number of beats heard in any assigned time will be equal to the number of complete vibrations which the one tone gains on the