A stretched wire of length 110cm is divided into three segments whose frequencies are in the ratio 1 : 2 : 3. Their length must be:

20cm, 30cm, 60cm

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60cm, 30cm, 20cm

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60cm, 20cm, 30cm

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30cm, 60cm, 20cm

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Solution

The correct option is B 60cm, 30cm, 20cm
$l_{1} + l_{2} + l_{3} = 110 n_{1} l_{1} = n_{2} l_{2} = n_{3} l_{3} \frac{n_{1}}{n_{2}} = \frac{1}{2} = \frac{l_{1}}{l_{2}}, \frac{n_{1}}{n_{3}} = \frac{1}{3} = \frac{l_{3}}{l_{1}} l_{1} + \frac{l_{1}}{2} + \frac{l_{1}}{3} = 11 l_{1} = 60 c m, l_{2} = 30 c m, l_{3} = 20 c m$

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