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ON INTERFERENCE.                            147
and 16 respectively, are heard together, 16 — 15 or 1 beat per second will be heard; that is, the number of beats per second, is equal to the difference of the vibration numbers. It is true, that 16 vibrations per second would not produce a musical sound, but that in no way affects the above reasoning. For suppose the vibration numbers of the forks to have been 160 and 150; the figure will represent the waves originated in one-twentieth of a second. Con­sequently in this case half a beat will be formed in one-twentieth of a second, or one beat in one-tenth of a second; that is, 10 = (160 — 150) beats per second. It is evident, therefore, that the number of beats per second, due to two simple tones, is equal to the difference of their respective vibration numbers.
For purposes of experimental study, wide stopped organ pipes are well adapted for the production of beats between simple tones; for when such pipes are gently blown, the fundamentals only are heard, or at most, accompanied by very faint third partials. If two exactly similar pipes be used, the tones produced will of course be in unison. To obtain beats, the pitch of one may be slightly lowered by shading the embouchure; or better still, one of the pipes intstead of being permanently closed at the top, may be stopped by a movable wooden piston, or plug, working air-tight in the pipe. After the pipes have been brought into unison, the pitch of the one may be varied to any desired extent, by moving the wooden piston, which alters the length of the vibrating air column. If the plug be moved very slightly from its unison position, very slow beats may be obtained, each beat lasting for a second or more. The crescendo and sub­sequent diminuendo of the beat is then very perceptible. By gradually moving the plug farther and farther from its unison position, the beats follow one another more and more rapidly, till at last they cease to be separately distinguishable.
The interference of two such organ pipes as the above, may be rendered visible by the use of the manometric flame apparatus shown in fig. 55. Instead of each tympanum having its own flame however, the outlet pipes from the two tympana unite into one (fig. 77), with a single flame at the end.