Text: The following table show the number of divisions a vibrating body divides itself and the ratio of frequencies generated. Bell as a disk Number of Divisions: 4, 6, 8, 10, 12 etc. Squares of vibration: 2, 3, 4, 5, 6 etc. Free Bar Number of Divisions: 2, 3, 4, 5, 6, 7 etc Squares of vibration: 3, 5, 7, 9, 11, 13 etc (approx) Fixed Rod (fixed at both ends) Number of Divisions 0, 1, 2, 3 etc Cycles per second 9, 25, 49, 81 etc Squares of vibration 3, 5, 7, 9 etc Fixed Rod (fixed at one end) Number of Divisions 0, 1, 2, 3, 4 etc Cycles per second 36, 225, 625, 1225, 2025 etc Squares of vibrations 6, 15, 25, 35, 45 etc For longitudinal as well as lateral the number of vibrations executed in a given time is inversely proportional to the length of the wire. The rates of vibration follow the order of numbers (of nodes) 1, 2, 3, 4, 5 etc. For longitudinal rods & bars the same as above. For longitudinal rods & bars fixed at one end. See page 192 of (6)

See Also: ACOUSTICS §14, 15, 16; TUBE RESONATOR, SPHERE, TONE-SIMPLE OR COMPOUND, LONGITUDINAL VIBRATIONS, HARMONIC & INHARMONIC, BEATS, LAW OF SUPERPOSITION, OVERTONE, POWER OF HARMONICS

Source: 6