Text: 1) The number of vibrations is inversely proportional to the length of the string. i.e.; 1/2 length = 2 x cps; 1/3 = 3 x cps, etc. 2) The number of vibrations is proportional to the square roots of the stretching weights. i.e.; 1 lb. = 1 cps; 4 lb. = 2 cps, 9 lb. = 3 cps. 3) The number of vibrations varies inversely as the thickness of the string. i.e.; 1 dia.= 1 cps; 2 x dia.= 1/2 cps; 3 x dia. = 1/3 cps 4) The number of vibrations is inversely proportional to the square root of the density of the string. i.e.; if density =1/4 of another string it will have 2 x cps, if density is 1/9 of another string it will have 3 x cps. 5) 3&4 together: The number of vibrations is inversely proportional to the square root of the weight of the string.

See Also: HARMONICS, RATES OF; ACOUSTICS § 14, 15, 16; LAW OF LINEAR DIMENSIONS; LAW OF VIBRATION

Source: