A sonometer wire is to be divided in to three segments having fundamental frequencies in the ratio $1 : 2 : 3$ . What should be the ratio of lengths?

4 : 2 : 1

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4 : 3 : 1

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6 : 3 : 2

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3 : 2 : 1

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Solution

The correct option is B $6 : 3 : 2$
$f = \frac{1}{2 L} \sqrt{\frac{T}{m}}$
i.e. , for same sonometer, for different segments of bridges length will be the tuning parameter.
we are given,
$f_{1} : f_{2} : f_{3} = 1 : 2 : 3$
while,
$f_{1} : f_{2} : f_{3} = \frac{1}{L_{1}} : \frac{1}{L_{2}} : \frac{1}{L_{3}}$
therefore $L_{1} : L_{2} : L_{3} = \frac{1}{f_{1}} : \frac{1}{f_{2}} : \frac{1}{f_{3}} = 6 : 3 : 2$

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A sonometer wire is to be divided in to three segments having fundamental frequencies in the ratio 1:2:3. What should be the ratio of lengths?

The correct option is B 6:3:2f=12L√Tm i.e. , for same sonometer, for different segments of bridges length will be the tuning parameter. we are given, f1:f2:f3=1:2:3 while, f1:f2:f3=1L1:1L2:1L3 therefore L1:L2:L3=1f1:1f2:1f3=6:3:2

A sonometer wire is to be divided in to three segments having fundamental frequencies in the ratio $1 : 2 : 3$ . What should be the ratio of lengths?