A sonometer wire of length 114 cm is fixed at both the ends. Where… | JEE Main 2013 (23 Apr, Shift 1)

Q104JEE Main 2013 · 23 APR · SHIFT 1Easy

Stationary Waves & Vibrating Strings

A sonometer wire of length 114 cm is fixed at both the ends. Where should the two bridges be placed so as to divide the wire into three segments whose fundamental frequencies are in the ratio 1: 3: 4?

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Answer: (d)

$f \propto \dfrac{1}{l}$ : $l_1 : l_2 : l_3 = 1 : \dfrac{1}{3} : \dfrac{1}{4} = 12 : 4 : 3$ .
Total parts $= 19$ , each part $= \dfrac{114}{19} = 6\text{ cm} \Rightarrow 72, 24, 18\text{ cm}$ .
Bridges at $72\text{ cm}$ and $72 + 24 = 96\text{ cm}$ from one end.
So the answer is (d) at 72 cm and 96 cm from one end.

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