A wire of length 2L, is made by joining two wires A and B of same… | JEE Main 2019 (8 Apr, Shift 1)

Q97JEE Main 2019 · 8 APR · SHIFT 1Difficult

Stationary Waves & Vibrating Strings

A wire of length 2L, is made by joining two wires A and B of same length but different radii r and 2r and made of the same material. It is vibrating at a frequency such that the joint of the two wires forms a node. If the number of antinodes in wire A is p and that in B is q then the ratio p: q is:

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Answer: (c)

Radii $r$ and $2r$ : $\mu_B=4\mu_A$ , so $v_A=2v_B$ .
Same $f$ , same length $L$ , joint a node: $f=\frac{p v_A}{2L}=\frac{q v_B}{2L}$ .
$\frac{p}{q}=\frac{v_B}{v_A}=\frac{1}{2}$ , so the answer is (c) $1:2$ .

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