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 BODS, PLATES, ETC. 125
strewing sand lightly and evenly over the plate before bowing. When a plate, thus treated, vibrates, the sand being violently agitated over the vibrating segments, is rapidly jerked away from these parts, and arranges itself along the nodal lines (fig. 64).
The simplest way in which a circular plate can vibrate, is in four segments (fig. 65, A); the next simplest in six segments (fig. 65, B);
the next in eight (fig. 65, C); and so on. Much more complicated figures, with nodal circles, may be obtained by stopping the plate at appropriate points and bowing accordingly.
Figure (66, A) shows the simplest way in which a square plate can vibrate, and (fig. 66, B) gives the next simplest form ; the note
ABC Fig. 66.
produced in the latter case being the fifth above that produced in the former. The sand figures become very complicated and beautiful as the tones rise in pitch ; (fig. 66, C) representing one of the least complex. Adjacent segments are always in different phases; that is, while one is above its ordinary position, the adjacent ones are below it. This can be proved experimentally, as will be subsequently shown.
Bells. Theoretically, a bell vibrates in the same way as a plate fixed at the centre. The simplest way in which it can vibrate is with four nodal lines, the tone thus produced being the fundamental. The