A sonometer wire of length 120 cm is divided into three segments of lengths in the ratio of 1:2:3. What is the ratio of their fundamental frequencies?

3:2:1

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4:2:1

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5:3:2

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6:3:2

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Solution

The correct option is D 6:3:2
The frequency of the fundamental mode is given by $f = \frac{1}{2 L} \sqrt{\frac{T}{μ}}$ .
$∴ f \propto \frac{1}{L}$
Hence, $f_{1} : f_{2} : f_{3} = \frac{1}{L_{1}} : \frac{1}{L_{2}} : \frac{1}{L_{3}}$
Now, $L_{1} = 20 c m, L_{2} = 40 c m, L_{3} = 60 c m$
Therefore, $f_{1} : f_{2} : f_{3} = \frac{1}{20} : \frac{1}{40} : \frac{1}{60} = 6 : 3 : 2$
Hence, the correct choice is (d).

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A sonometer wire of length 120 cm is divided into three segments of lengths in the ratio of 1:2:3. What is the ratio of their fundamental frequencies?

The correct option is D 6:3:2The frequency of the fundamental mode is given by f=12L√Tμ. ∴f∝1L Hence, f1:f2:f3=1L1:1L2:1L3 Now, L1=20 cm,L2=40 cm,L3=60 cm Therefore, f1:f2:f3=120:140:160=6:3:2 Hence, the correct choice is (d).