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Two strings of the same material and the same area of cross – section are used in sonometer experiment. One is loaded with 12kg and the other with 3 kg. The fundamental frequency of the first string is equal to the first overtone of the second string. If the length of the second string is 100 cm, then the length of the first string is

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300 cm

200 cm

100 cm

50 cm

answer is C.

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Detailed Solution

$\frac{1}{2 l_{1}} \sqrt{\frac{M_{1} g}{Ad}} = \frac{2}{2 l_{2}} \sqrt{\frac{M_{2} g}{Ad}} \frac{l_{1}}{l_{2}} = \frac{1}{2} \sqrt{\frac{M_{1}}{M_{2}}} = 1; l_{2} = l_{1} = 100 cm$

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