Page:Elementary Text-book of Physics (Anthony, 1897).djvu/195

§ 155] the simpler forms of these curves. The figures of the upper line are those produced by two forks in unison; those of the second line by two forks of which the vibration numbers are as 2:1; those of the lower line by two forks of which the vibration numbers are as 3:2.

155. Beats.—It has already been explained (§139) that, when two tones of nearly the same pitch are sounded together, variations of intensity, called beats, are heard. Helmholtz's theory of the perception of beats was, that, of the little fibres in the ear which are tuned so as to vibrate with the various tones, those which are nearly in unison affect one another so as to increase and diminish one another's motions, and hence that no beats could be perceived unless the tones were nearly in unison. Beats are, however, heard when a tone and its octave are not quite in tune, and, in general, a tone making $$n$$ vibrations produces $$m$$ beats when sounded with a tone making $$2n \pm m, 3m \pm m,$$ etc., vibrations. This was explained in accordance with Helmholtz's theory, by assuming that one of the harmonics of the lower tone, which is nearly in unison with the upper, causes the beats, or, in cases where this is inadmissible, that they are caused by the lower tone in conjunction with a resultant