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تسجيل

Laws of the Vibration of Strings

المؤلف:  GEORGE A. HOADLEY

المصدر:  ESSENTIALS OF PHYSICS

الجزء والصفحة:  p-221

2025-11-19

487

1.  The tension and mass per unit length being the same, the number of vibrations per second varies inversely as the length of the string.
2. The length and tension being the same, the number of vibration per second varies inversely as the square root of the mass per unit length of the string.
3. The length and mass per unit length being the saтe, the number of vibrations per second varies directly as the square root of the tension.

The above laws can be expressed by the proportion  

For the first law, under the conditions given, the proportion becomes

If the length of a certain string is taken as unity the parts of the same string that give the other tones of the scale are as follows:

It will be observed that these ratios which give the relative length of string are the reciprocals of the ratios giving the relative numbers of vibrations.

For the second law the proportion becomes

and for the third law,  These laws can be verified on the sonometer. The strings of the piano illustrate the preceding laws. The lowest tones are made by long, heavy strings without great tension, while the highest tones are made by short, light strings stretched to a high tension.