HANDBOOK OF ACOUSTICS - online book

A complete view of Acoustical Science & its bearings on music, for musicians & music students.

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ON THE VIBRATIONS OF STRINGS.               93
A stretched string can therefore vibrate as a whole, that is, with one ventral segment, or with two, three, four, five, six, or more ventral segments, hut not with any intermediate fraction. Now if we call the note given forth by a string, when its whole length is vibrating (d|) ; we have already learnt, that when its two halves only are vibrating, we get the octave above, (d) ; if it vibrate in three ventral segments we shall get the twelfth above, (s); with four segments, (d1); with five,; and so on. Only those notes belong­ing to the series 1, 2, 3, 4, 5, &c, can occur; no note intermediate between these can be produced. It will be at once observed, that this is the series of partial tones, and the idea at once suggests itself, that the occurrence of partials in the tones of stringed instru­ments is due to the fact, that a string not only vibrates as a whole, but at the same time in halves, thirds, quarters, &c, each segment giving rise to a simple sound of its own particular pitch.
The student may convince himself that this is really the case, by a variety of experiments. Thus, while a string is vibrating and giving forth a compound tone in which the fifth partial can be heard, lightly touch it with a feather at a point, distant 1 of its length from the end; all the partials except the fifth, which has a node at this point, will rapidly die out, but this one will be plainly heard, showing that the string must have been vibrating in five segments. Again, touch the middle of the string in a similar manner, after setting it in vibration, and all the partials except those which require a node at this point will vanish, that is, only the second, fourth, sixth, &c, will remain. Further, pluck the string at its middle point; all the tones which require a node at this point must then be absent, only the first, third, fifth, seventh, &c, being heard. In this way, the presence or absence of any par­ticular partial of a compound tone may be ensured.
The occurrence and relative intensities of partials on stringed instruments, depend upon :—
1st. The nature of the string.
2nd. The kind of hammer, bowing, plectrum, &c.
3rd. The place where the string is struck, bowed, or plucked.