When a circular plate clamped at its centre sounds its fundamental tone, it divides into four vibrating parts, separated by four radial nodal lines.
The next note of the plate corresponds to a division into six vibrating sectors, the next note to a division into eight sectors; such a plate can divide into any even number of vibrating sectors, the sand-figures assuming beautiful stellar forms.
The rates of vibration corresponding to the divisions of a disk are represented by the squares of the numbers 2, 3, 4, 5, 6, etc. In other words, the rates of vibration are proportional to the squares of the numbers representing the sectors into which the disk is divided.
When a bell sounds its deepest note it is divided into four vibrating parts separated from each other by nodal lines, which run upward from the sound-bow and cross each other at the crown.
It is capable of the same subdivisions as a disk; the succession of its tones being also the same.
The rate of vibration of a disk or bell is directly proportional to the thickness and inversely proportional to the square of the diameter.
CHAPTER V
Longitudinal Vibrations of a Wire—Relative Velocities of Sound in Brass and Iron—Longitudinal Vibrations of Rods fixed at One End—Of Rods free at Both Ends—Divisions and Overtones of Rods vibrating longitudinally—Examination of Vibrating Bars by Polarized Light—Determination of Velocity of Sound in Solids—Resonance—Vibrations of Stopped Pipes: their Divisions and Overtones—Relation of the Tones of Stopped Pipes to those of Open Pipes—Condition of Column of Air within a Sounding Organ-Pipe—Reeds and Reed-Pipes—The Voice—Overtones of the Vocal Chords—The Vowel Sounds—Kundt’s Experiments—New Methods of determining the Velocity of Sound