GALILEO REGARDING MUSICAL STRINGS

Galileo observed that the frequency of a musical string may be changed to that of a higher note by  

The meaning of size is not elear, although it may be assumed to be diameter and may be eheeked by dimensional analysis. 

At the outset, the frequency of a plucked string might be assumed to vary with the variables listed in Table 7.3. That is  

This is in agreement with Eq. (7.15), provided size is interpreted as pcf (the mass of the string per unit length) instead of diameter d). The modulus is seen to cancel. This is because Galileo probably used a single material in obtaining the results expressed in Eq. (7.15). If different materials were to be used, the same frequency would be obtained, provided W or d or both were varied, with E such that Wld E remained unchanged. 

Theoretically, the constant K may be shown to be 0.5 for ideal end conditions. Results given in Table 7.4 were obtained for experiments in which weights were hung on wires of different diameters stretched over pins of variable spacing ) (Fig. 7.3) until the frequency of the string was either middle C (256 Hz) or twice this frequency. In all cases, the wires were of steel with p = 72.5 x 10 lb in. sec. Tuning forks and a person with a musically sensitive ear were used in obtaining the data of Table 7.4. The mean value ofK from these experiments was found to be 0.32. This differs from the value 0.5 due primarily to friction between the wires and the pins. 

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