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MHT CET 2021 (20 Sep, Shift 1) · Stationary Waves & Vibrating Strings

Stationary Waves & Vibrating Strings question from MHT CET 2021 (20 Sep, Shift 1)

Q80MHT CET 2021 · 20 SEP · SHIFT 1Difficult

Stationary Waves & Vibrating Strings

Two wires of same material of radius 'r' and '2r' respectively are welded together end to end. The combination is then used as a sonometer wire under tension 'T'. The joint is kept midway between the two bridges. The ratio of the number of loops formed in the wires such that the joint is a node is

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Answer: (b)

$\mu=\pi r^2 d \Rightarrow \mu_2=4\mu_1$ , so $v=\sqrt{T/\mu}$ gives $v_1=2v_2$ .
Same frequency and same length $l$ for both parts: $n=\frac{p v}{2l} \Rightarrow p \propto \frac{1}{v}$ .
$p_1:p_2=1:2$ , so the answer is (b) $1:2$ .

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