Beats

BEATS, periodic changes in the magnitude of amplitude during various kinds of oscillations. They usually arise during oscillations of coupled systems. Thus, if two pendulums are suspended side by side, and their rods (or threads, if the pendulum is a weight suspended on a thread) are connected

to each other by means of a thin thread and a small weight is suspended from the latter, beats can be clearly observed in such a system. If one of the pendulums is set swinging, it will act through the connecting thread on the second, stationary pendulum. The latter will gradually begin to swing, thereby taking energy away from the first pendulum. If both pendulums are tuned to resonance, that is, their periods of free oscillation are equal, the energy of the first pendulum can ultimately be completely transferred to the second, after which the process will begin in reverse order: energy will

pass from the second pendulum to the first. As a result, the oscillations of both pendulums will proceed according to the law graphically depicted in the figure. The upper part of the figure depicts the oscillations of the first pendulum, and the lower part, those of the second. Beats, among other things, occur during the simultaneous sounding of two sound sources having close oscillation periods. As a result of the superposition of such oscillations, an extremely unpleasant periodic amplification and attenuation of sound is produced. Since the number of beats per second is equal to the difference in the number of vibrations corresponding to one and the other sound, their character must obviously depend on the degree of closeness between these numbers. Helmholtz showed that, based on this principle, one can build the theory of consonance (pleasant combination of sounds) and dissonance (unpleasant combination).