Two wires W1 and W2 have the same radius r and respective densities ρ… | JEE Main 2017 (8 Apr, Shift 1)

Q99JEE Main 2017 · 8 APR · SHIFT 1Difficult

Stationary Waves & Vibrating Strings

Two wires W1 and W2 have the same radius r and respective densities $\rho$ 1 and $\rho$ 2 such that ρ2 = 4 $\rho$ 1. They are joined together at the point O, as shown in the figure. The combination is used as a sonometer wire and kept under tension T. The point O is midway between the two bridges. When a stationary wave is set up in the composite wire, the joint is found to be a node. The ratio of the number of antinodes formed in W1 to W2 is:

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Answer: (b)

Same radius: $\mu \propto \rho$ , so $\mu_2=4\mu_1$ and $v_1=2v_2$ .
Equal lengths, same frequency, joint a node: $p \propto \frac{1}{v}$ .
$p_1:p_2=1:2$ , so the answer is (b).

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